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For 1 ≤ p &lt; ∞, denote by Ap(G) the space of integrable functions on G whose Fourier transforms belong to lp(Γ). We investigate several problems related to multipliers from Ap(G) to Aq(G). In" /> <meta name="twitter:image" content="http://a.academia-assets.com/images/twitter-card.jpeg" /> <meta property="fb:app_id" content="2369844204" /> <meta property="og:type" content="article" /> <meta property="og:url" content="https://www.academia.edu/49544872/Multipliers_on_spaces_of_functions_on_compact_groups_with_p_summable_Fourier_transforms" /> <meta property="og:title" content="Multipliers on spaces of functions on compact groups with p-summable Fourier transforms" /> <meta property="og:image" content="http://a.academia-assets.com/images/open-graph-icons/fb-paper.gif" /> <meta property="og:description" content="Let G be a compact abelian group with dual group Γ. For 1 ≤ p &lt; ∞, denote by Ap(G) the space of integrable functions on G whose Fourier transforms belong to lp(Γ). We investigate several problems related to multipliers from Ap(G) to Aq(G). In" /> <meta property="article:author" content="https://independent.academia.edu/sanjivgupta21" /> <meta name="description" content="Let G be a compact abelian group with dual group Γ. For 1 ≤ p &lt; ∞, denote by Ap(G) the space of integrable functions on G whose Fourier transforms belong to lp(Γ). We investigate several problems related to multipliers from Ap(G) to Aq(G). In" /> <title>(PDF) Multipliers on spaces of functions on compact groups with p-summable Fourier transforms | sanjiv gupta - Academia.edu</title> <link rel="canonical" href="https://www.academia.edu/49544872/Multipliers_on_spaces_of_functions_on_compact_groups_with_p_summable_Fourier_transforms" /> <script async src="https://www.googletagmanager.com/gtag/js?id=G-5VKX33P2DS"></script> <script> window.dataLayer = window.dataLayer || []; function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'G-5VKX33P2DS', { cookie_domain: 'academia.edu', send_page_view: false, }); gtag('event', 'page_view', { 'controller': "single_work", 'action': "show", 'controller_action': 'single_work#show', 'logged_in': 'false', 'edge': 'unknown', // Send nil if there is no A/B test bucket, in case some records get logged // with missing data - that way we can distinguish between the two cases. // ab_test_bucket should be of the form <ab_test_name>:<bucket> 'ab_test_bucket': null, }) </script> <script> var $controller_name = 'single_work'; var $action_name = "show"; var $rails_env = 'production'; var $app_rev = '92477ec68c09d28ae4730a4143c926f074776319'; var $domain = 'academia.edu'; var $app_host = "academia.edu"; var $asset_host = "academia-assets.com"; var $start_time = new Date().getTime(); var $recaptcha_key = "6LdxlRMTAAAAADnu_zyLhLg0YF9uACwz78shpjJB"; var $recaptcha_invisible_key = "6Lf3KHUUAAAAACggoMpmGJdQDtiyrjVlvGJ6BbAj"; var $disableClientRecordHit = false; </script> <script> window.require = { config: function() { return function() {} } } </script> <script> window.Aedu = window.Aedu || {}; window.Aedu.hit_data = null; window.Aedu.serverRenderTime = new Date(1732772351000); window.Aedu.timeDifference = new Date().getTime() - 1732772351000; </script> <script type="application/ld+json">{"@context":"https://schema.org","@type":"ScholarlyArticle","abstract":"Let G be a compact abelian group with dual group Γ. For 1 ≤ p \u0026amp;amp;amp;lt; ∞, denote by Ap(G) the space of integrable functions on G whose Fourier transforms belong to lp(Γ). We investigate several problems related to multipliers from Ap(G) to Aq(G). In particular, we prove that (Ap, Ap) ⊊ (Aq, Aq). For the circle group, we characterise permutation invariant multipliers from Ap to Ar for 1 ≤ r ≤ 2.","author":[{"@context":"https://schema.org","@type":"Person","name":"sanjiv gupta"}],"contributor":[],"dateCreated":"2021-07-04","dateModified":"2021-09-12","datePublished":"1993-01-01","headline":"Multipliers on spaces of functions on compact groups with p-summable Fourier transforms","inLanguage":"en","keywords":["Pure Mathematics","Fourier transform"],"locationCreated":null,"publication":"Bulletin of the Australian Mathematical Society","publisher":{"@context":"https://schema.org","@type":"Organization","name":"Cambridge University Press (CUP)"},"image":null,"thumbnailUrl":null,"url":"https://www.academia.edu/49544872/Multipliers_on_spaces_of_functions_on_compact_groups_with_p_summable_Fourier_transforms","sourceOrganization":[{"@context":"https://schema.org","@type":"EducationalOrganization","name":null}]}</script><link rel="stylesheet" media="all" 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For 1 ≤ p \u0026lt; ∞, denote by Ap(G) the space of integrable functions on G whose Fourier transforms belong to lp(Γ). We investigate several problems related to multipliers from Ap(G) to Aq(G). In particular, we prove that (Ap, Ap) ⊊ (Aq, Aq). For the circle group, we characterise permutation invariant multipliers from Ap to Ar for 1 ≤ r ≤ 2.","publisher":"Cambridge University Press (CUP)","publication_date":"1993,,","publication_name":"Bulletin of the Australian Mathematical Society"},"document_type":"paper","pre_hit_view_count_baseline":null,"quality":"high","language":"en","title":"Multipliers on spaces of functions on compact groups with p-summable Fourier transforms","broadcastable":true,"draft":null,"has_indexable_attachment":true,"indexable":true}}["work"]; window.loswp.workCoauthors = [152333134]; window.loswp.locale = "en"; window.loswp.countryCode = "SG"; window.loswp.cwvAbTestBucket = ""; window.loswp.designVariant = "ds_vanilla"; window.loswp.fullPageMobileSutdModalVariant = "full_page_mobile_sutd_modal"; window.loswp.useOptimizedScribd4genScript = false; window.loswp.appleClientId = 'edu.academia.applesignon';</script><script defer="" src="https://accounts.google.com/gsi/client"></script><div class="ds-loswp-container"><div class="ds-work-card--grid-container"><div class="ds-work-card--container js-loswp-work-card"><div class="ds-work-card--cover"><div class="ds-work-cover--wrapper"><div class="ds-work-cover--container"><button class="ds-work-cover--clickable js-swp-download-button" data-signup-modal="{"location":"swp-splash-paper-cover","attachmentId":67873285,"attachmentType":"pdf"}"><img alt="First page of “Multipliers on spaces of functions on compact groups with p-summable Fourier transforms”" class="ds-work-cover--cover-thumbnail" src="https://0.academia-photos.com/attachment_thumbnails/67873285/mini_magick20210704-5819-1596feu.png?1625459050" /><img alt="PDF Icon" class="ds-work-cover--file-icon" src="//a.academia-assets.com/assets/single_work_splash/adobe.icon-574afd46eb6b03a77a153a647fb47e30546f9215c0ee6a25df597a779717f9ef.svg" /><div class="ds-work-cover--hover-container"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span><p>Download Free PDF</p></div><div class="ds-work-cover--ribbon-container">Download Free PDF</div><div class="ds-work-cover--ribbon-triangle"></div></button></div></div></div><div class="ds-work-card--work-information"><h1 class="ds-work-card--work-title">Multipliers on spaces of functions on compact groups with p-summable Fourier transforms</h1><div class="ds-work-card--work-authors ds-work-card--detail"><a class="ds-work-card--author js-wsj-grid-card-author ds2-5-body-md ds2-5-body-link" data-author-id="152333134" href="https://independent.academia.edu/sanjivgupta21"><img alt="Profile image of sanjiv gupta" class="ds-work-card--author-avatar" src="//a.academia-assets.com/images/s65_no_pic.png" />sanjiv gupta</a></div><div class="ds-work-card--detail"><p class="ds-work-card--detail ds2-5-body-sm">1993, Bulletin of the Australian Mathematical Society</p></div><p class="ds-work-card--work-abstract ds-work-card--detail ds2-5-body-md">Let G be a compact abelian group with dual group Γ. For 1 ≤ p &lt; ∞, denote by Ap(G) the space of integrable functions on G whose Fourier transforms belong to lp(Γ). We investigate several problems related to multipliers from Ap(G) to Aq(G). In particular, we prove that (Ap, Ap) ⊊ (Aq, Aq). For the circle group, we characterise permutation invariant multipliers from Ap to Ar for 1 ≤ r ≤ 2.</p><div class="ds-work-card--button-container"><button class="ds2-5-button js-swp-download-button" data-signup-modal="{"location":"continue-reading-button--work-card","attachmentId":67873285,"attachmentType":"pdf","workUrl":"https://www.academia.edu/49544872/Multipliers_on_spaces_of_functions_on_compact_groups_with_p_summable_Fourier_transforms"}">See full PDF</button><button class="ds2-5-button ds2-5-button--secondary js-swp-download-button" data-signup-modal="{"location":"download-pdf-button--work-card","attachmentId":67873285,"attachmentType":"pdf","workUrl":"https://www.academia.edu/49544872/Multipliers_on_spaces_of_functions_on_compact_groups_with_p_summable_Fourier_transforms"}"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span>Download PDF</button></div></div></div></div><div data-auto_select="false" data-client_id="331998490334-rsn3chp12mbkiqhl6e7lu2q0mlbu0f1b" data-doc_id="67873285" data-landing_url="https://www.academia.edu/49544872/Multipliers_on_spaces_of_functions_on_compact_groups_with_p_summable_Fourier_transforms" data-login_uri="https://www.academia.edu/registrations/google_one_tap" data-moment_callback="onGoogleOneTapEvent" id="g_id_onload"></div><div class="ds-top-related-works--grid-container"><div class="ds-related-content--container ds-top-related-works--container"><h2 class="ds-related-content--heading">Related papers</h2><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="0" data-entity-id="54535373" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/54535373/On_the_vector_Fourier_multipliers_for_compact_groups">On the vector Fourier multipliers for compact groups</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="172262998" href="https://independent.academia.edu/YaoganMensah">Yaogan Mensah</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Open Journal of Mathematical Sciences</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"On the vector Fourier multipliers for compact groups","attachmentId":70854259,"attachmentType":"pdf","work_url":"https://www.academia.edu/54535373/On_the_vector_Fourier_multipliers_for_compact_groups","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/54535373/On_the_vector_Fourier_multipliers_for_compact_groups"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="1" data-entity-id="54535363" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/54535363/Completely_Bounded_Fourier_Multipliers_Over_Compact_Groups">Completely Bounded Fourier Multipliers Over Compact Groups</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="172262998" href="https://independent.academia.edu/YaoganMensah">Yaogan Mensah</a></div><p class="ds-related-work--abstract ds2-5-body-sm">Vector version of Fourier multipliers over compact non necessary abelian groups are defined. 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class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/29436596/Smooth_Fourier_multipliers_on_group_von_Neumann_algebras"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="8" data-entity-id="72846672" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/72846672/Smooth_Fourier_multipliers_in_group_algebras_via_Sobolev_dimension">Smooth Fourier multipliers in group algebras via Sobolev dimension</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="146358351" href="https://independent.academia.edu/JungeM">Marius Junge</a></div><p class="ds-related-work--abstract ds2-5-body-sm">We investigate Fourier multipliers with smooth symbols defined over locally compact Hausdorff groups. Our main results in this paper establish new H\&quot;ormander-Mikhlin criteria for spectral and non-spectral multipliers. The key novelties which shape our approach are three. First, we control a broad class of Fourier multipliers by certain maximal operators in noncommutative $L_p$ spaces. This general principle ---exploited in Euclidean harmonic analysis during the last 40 years--- is of independent interest and might admit further applications. Second, we replace the formerly used cocycle dimension by the Sobolev dimension. This is based on a noncommutative form of the Sobolev embedding theory for Markov semigroups initiated by Varopoulos, and yields more flexibility to measure the smoothness of the symbol. Third, we introduce a dual notion of polynomial growth to further exploit our maximal principle for non-spectral Fourier multipliers. The combination of these ingredients yiel...</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Smooth Fourier multipliers in group algebras via Sobolev dimension","attachmentId":83901654,"attachmentType":"pdf","work_url":"https://www.academia.edu/72846672/Smooth_Fourier_multipliers_in_group_algebras_via_Sobolev_dimension","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/72846672/Smooth_Fourier_multipliers_in_group_algebras_via_Sobolev_dimension"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="9" data-entity-id="69303702" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/69303702/A_convolution_type_characterization_for_Lp_multipliers_for_the_Heisenberg_group">A convolution type characterization for Lp - multipliers for the Heisenberg group</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="40744682" href="https://independent.academia.edu/AKVijayarajan">A K Vijayarajan</a></div><p class="ds-related-work--metadata ds2-5-body-xs">2007</p><p class="ds-related-work--abstract ds2-5-body-sm">It is well known that if m is an Lp - multiplier for the Fourier transform on ℝn(1&lt;p&lt;∞) , then there exists a pseudomeasure σ such that Tmf =σ*f. A similar result is proved for the group Fourier transform on the Heisenberg group Hn. Though this result is already known in generality for amenable groups, a simple proof is provided in this paper.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"A convolution type characterization for Lp - multipliers for the Heisenberg group","attachmentId":79450949,"attachmentType":"pdf","work_url":"https://www.academia.edu/69303702/A_convolution_type_characterization_for_Lp_multipliers_for_the_Heisenberg_group","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/69303702/A_convolution_type_characterization_for_Lp_multipliers_for_the_Heisenberg_group"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div></div></div><div class="ds-sticky-ctas--wrapper js-loswp-sticky-ctas hidden"><div class="ds-sticky-ctas--grid-container"><div class="ds-sticky-ctas--container"><button class="ds2-5-button js-swp-download-button" data-signup-modal="{"location":"continue-reading-button--sticky-ctas","attachmentId":67873285,"attachmentType":"pdf","workUrl":null}">See full PDF</button><button class="ds2-5-button ds2-5-button--secondary js-swp-download-button" data-signup-modal="{"location":"download-pdf-button--sticky-ctas","attachmentId":67873285,"attachmentType":"pdf","workUrl":null}"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span>Download PDF</button></div></div></div><div class="ds-below-fold--grid-container"><div class="ds-work--container js-loswp-embedded-document"><div class="attachment_preview" data-attachment="Attachment_67873285" style="display: none"><div class="js-scribd-document-container"><div class="scribd--document-loading js-scribd-document-loader" style="display: block;"><img alt="Loading..." src="//a.academia-assets.com/images/loaders/paper-load.gif" /><p>Loading Preview</p></div></div><div style="text-align: center;"><div class="scribd--no-preview-alert js-preview-unavailable"><p>Sorry, preview is currently unavailable. 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ds2-5-body-link" href="https://www.academia.edu/103541551/Fourier_Multipliers_for_L_p_on_Ch%C3%A9bli_Trim%C3%A8che_Hypergroups">Fourier Multipliers for L p on Chébli-Trimèche Hypergroups</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="40193071" href="https://murdoch.academia.edu/WalterBloom">Walter R Bloom</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Proceedings of the London Mathematical Society, 2000</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Fourier Multipliers for L p on Chébli-Trimèche Hypergroups","attachmentId":103521514,"attachmentType":"pdf","work_url":"https://www.academia.edu/103541551/Fourier_Multipliers_for_L_p_on_Ch%C3%A9bli_Trim%C3%A8che_Hypergroups","alternativeTracking":true}"><span class="material-symbols-outlined" 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ds2-5-body-sm ds2-5-body-link" data-author-id="8473117" href="https://independent.academia.edu/Micha%C5%82Wojciechowski">Michał Wojciechowski</a></div><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"On the isomorphisms of Fourier algebras of finite abelian groups","attachmentId":32809048,"attachmentType":"pdf","work_url":"https://www.academia.edu/5789218/On_the_isomorphisms_of_Fourier_algebras_of_finite_abelian_groups","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/5789218/On_the_isomorphisms_of_Fourier_algebras_of_finite_abelian_groups"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="8" data-entity-id="63231866" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/63231866/Multipliers_of_Group_Algebras_of_Vector_Valued_Functions">Multipliers of Group Algebras of Vector-Valued Functions</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="51611661" href="https://iiitg.academia.edu/MalayDutta">Malay A Dutta</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Proceedings of the American Mathematical Society, 1981</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" 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