Essential norms and Schatten(-Herz) classes of integration operators from Bergman spaces to Hardy spaces

Essential norms and Schatten(-Herz) classes of integration operators from Bergman spaces to Hardy spaces | 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 Essential norms and Schatten(-Herz) classes of integration operators from Bergman spaces to Hardy spaces Jiale Chen, Jordi Pau, Maofa Wang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-357094/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 11 Apr, 2021 Read the published version in Results in Mathematics → Version 1 posted You are reading this latest preprint version Abstract In this paper, we completely characterize the compactness of the Volterra type integration operators J b acting from weighted Bergman spaces A p a to Hardy spaces H q for all 0 < p; q H q in the case 0 < p < q < 1. We finally describe the membership in the Schatten(-Herz) class of the Volterra type integration operators. Applied Mathematics Schatten(-Herz) classes essential norms integration operators Full Text Cite Share Download PDF Status: Published Journal Publication published 11 Apr, 2021 Read the published version in Results in Mathematics → 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. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-357094","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":18196313,"identity":"6d79c818-a82e-409e-8385-9d9018e5787a","order_by":0,"name":"Jiale Chen","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA4ElEQVRIiWNgGAWjYBACxmYGxgMMDEDE3sAGFmggQgsDRAvPASK1gABEi0QCkVqY25kfHPhQc0fOXPKN2WMeBhvZDQeYnz3A7zA2g4Mzjj0ztpydY27Mw5BmvOEAm7kBAb8YHOZtOJy44XbuNmkeBiDjAA+bBH4t7B8O/204XL/h5lmQlv/EaOExOMzYcDjB4AYvSMsBorQUHOw5dthww5n8b5JzDJKNZx5mM8OrxbD/+MYHP2oOyxscP5Ym8abCTrbvePMz/FoaULigoGLGpx4I5AnIj4JRMApGwShgYAAAXcJOm9vYD2sAAAAASUVORK5CYII=","orcid":"https://orcid.org/0000-0001-7700-5326","institution":"Wuhan University","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Jiale","middleName":"","lastName":"Chen","suffix":""},{"id":18196314,"identity":"23914c81-4fa4-43e4-9f78-1f94f1b12d58","order_by":1,"name":"Jordi Pau","email":"","orcid":"","institution":"Universitat de Barcelona","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Jordi","middleName":"","lastName":"Pau","suffix":""},{"id":18196315,"identity":"e8ab0b7c-d830-4110-9a75-3f9c76ea6e7f","order_by":2,"name":"Maofa Wang","email":"","orcid":"","institution":"Wuhan University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Maofa","middleName":"","lastName":"Wang","suffix":""}],"badges":[],"createdAt":"2021-03-24 09:17:21","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-357094/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-357094/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s00025-021-01403-8","type":"published","date":"2021-04-11T19:07:48+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":13682400,"identity":"7554f886-bf4b-428d-928d-599a0121d42a","added_by":"auto","created_at":"2021-09-17 11:57:05","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":114662,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-357094/v1/c7fc1508-0d29-42cc-983d-6c2572413f51.pdf"}],"financialInterests":"","formattedTitle":"Essential norms and Schatten(-Herz) classes of integration operators from Bergman spaces to Hardy spaces","fulltext":[{"header":"Full Text","content":"\u003cp\u003eThis preprint is available for \u003ca href='/article/rs-357094/latest.pdf' target='_blank'\u003edownload as a PDF\u003c/a\u003e.\u003c/p\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"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":"Schatten(-Herz) classes, essential norms, integration operators","lastPublishedDoi":"10.21203/rs.3.rs-357094/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-357094/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn this paper, we completely characterize the compactness of the\u0026nbsp;Volterra type integration operators J\u003csub\u003eb\u003c/sub\u003e acting from weighted Bergman spaces\u0026nbsp;A\u003csup\u003ep\u003c/sup\u003e\u003csub\u003ea\u003c/sub\u003e\u0026nbsp;to Hardy spaces H\u003csup\u003eq\u003c/sup\u003e for all 0 \u0026lt; p; q \u0026lt; 1. Furthermore, we give some\u0026nbsp;estimates for the essential norms of J\u003csub\u003eb\u003c/sub\u003e :\u0026nbsp;A\u003csup\u003ep\u003c/sup\u003e\u003csub\u003ea\u003c/sub\u003e\u0026nbsp;-\u0026gt;\u0026nbsp;H\u003csup\u003eq\u003c/sup\u003e in the case 0 \u0026lt; p\u0026nbsp;\u0026lt; q \u0026lt; 1.\u0026nbsp;We finally describe the membership in the Schatten(-Herz) class of the Volterra type integration operators.\u003c/p\u003e","manuscriptTitle":"Essential norms and Schatten(-Herz) classes of integration operators from Bergman spaces to Hardy spaces","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2021-03-24 19:17:23","doi":"10.21203/rs.3.rs-357094/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","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}}],"origin":"","ownerIdentity":"aabdc6bd-73d4-4bb9-b872-c8fd33b530a0","owner":[],"postedDate":"March 24th, 2021","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":3196613,"name":"Applied Mathematics"}],"tags":[],"updatedAt":"2021-08-18T19:25:50+00:00","versionOfRecord":{"articleIdentity":"rs-357094","link":"https://doi.org/10.1007/s00025-021-01403-8","journal":{"identity":"results-in-mathematics","isVorOnly":false,"title":"Results in Mathematics"},"publishedOn":"2021-04-11 19:07:48","publishedOnDateReadable":"April 11th, 2021"},"versionCreatedAt":"2021-03-24 19:17:23","video":"","vorDoi":"10.1007/s00025-021-01403-8","vorDoiUrl":"https://doi.org/10.1007/s00025-021-01403-8","workflowStages":[]},"version":"v1","identity":"rs-357094","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-357094","identity":"rs-357094","version":["v1"]},"buildId":"rHA-KDH7Qsr4HCuvH75dn","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}