Complex symmetry of multiplication and composition operators on A12(D)

Complex symmetry of multiplication and composition operators on A12(D) | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Complex symmetry of multiplication and composition operators on A 1 2 (D) Anuradha Gupta, Deepika Singh This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4121651/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract For the set consisting of holomorphic functions over unit disk D whose derivativelies in the Bergman space A 2 (D) as well as in the classical Hardy space H 2 (D),we define a norm which is equivalent to the norm on the derivative Hardy space.We denote this space by A 1 2 (D). First, we’ll study some basic analytic propertiesof A 1 2 (D) and then obtain some characterizations of continuous multiplicationoperators on A 1 2 (D). In the last section, complex symmetries of composition operators on A 1 2 (D) with respect to a specific conjugation called standard conjugationare discussed. MSC[2020]: 47B33, 47B38 Complex symmetry Composition operator Derivative Hardy space Multiplication operator. Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4121651","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":281112393,"identity":"e458a089-9b6d-4cc9-b747-bdea99bee5af","order_by":0,"name":"Anuradha Gupta","email":"","orcid":"","institution":"University of Delhi","correspondingAuthor":false,"prefix":"","firstName":"Anuradha","middleName":"","lastName":"Gupta","suffix":""},{"id":281112395,"identity":"0c958709-7443-48e0-a776-7b9be9d8806e","order_by":1,"name":"Deepika Singh","email":"data:image/png;base64,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","orcid":"","institution":"University of Delhi","correspondingAuthor":true,"prefix":"","firstName":"Deepika","middleName":"","lastName":"Singh","suffix":""}],"badges":[],"createdAt":"2024-03-18 09:06:37","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4121651/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4121651/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":53865219,"identity":"daf3623d-4c1d-4ff7-a765-294c74ecd51e","added_by":"auto","created_at":"2024-04-01 13:55:31","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":255202,"visible":true,"origin":"","legend":"","description":"","filename":"ZIPCAOT.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4121651/v1_covered_4fc9ee5f-7a11-4a15-969b-b00312af9005.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"\u003cp\u003eComplex symmetry of multiplication and composition operators on A\u003csub\u003e1\u003c/sub\u003e\u003csup\u003e2\u003c/sup\u003e(D)\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Complex symmetry, Composition operator, Derivative Hardy space, Multiplication operator.","lastPublishedDoi":"10.21203/rs.3.rs-4121651/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4121651/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eFor the set consisting of holomorphic functions over unit disk D whose derivativelies in the Bergman space \u003cem\u003e\u003cstrong\u003eA\u003c/strong\u003e\u003c/em\u003e\u003csup\u003e2\u003c/sup\u003e(D) as well as in the classical Hardy space \u003cem\u003e\u003cstrong\u003eH\u003c/strong\u003e\u003c/em\u003e\u003csup\u003e2\u003c/sup\u003e(D),we define a norm which is equivalent to the norm on the derivative Hardy space.We denote this space by \u003cem\u003e\u003cstrong\u003eA\u003c/strong\u003e\u003c/em\u003e\u003csup\u003e1\u003c/sup\u003e\u003csub\u003e2\u003c/sub\u003e(D). 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