The Restriction Operator on Bergman Spaces
Motivated by questions related to the compactness of the ∂ ¯ -Neumann operator, we study the restriction operator from the Bergman space of a domain in C n to the Bergman space of a non-empty open subset of the domain. We relate the restriction operator to the Toeplitz operator on the Bergman space...
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| Veröffentlicht in: | The Journal of Geometric Analysis 2020-04, Vol.30 (2), p.2157-2188 |
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| container_title | The Journal of Geometric Analysis |
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| creator | Chakrabarti, Debraj Şahutoğlu, Sönmez |
| description | Motivated by questions related to the compactness of the
∂
¯
-Neumann operator, we study the restriction operator from the Bergman space of a domain in
C
n
to the Bergman space of a non-empty open subset of the domain. We relate the restriction operator to the Toeplitz operator on the Bergman space of the domain whose symbol is the characteristic function of the subset. Using the biholomorphic invariance of the spectrum of the associated Toeplitz operator, we study the restriction operator from the Bergman space of the unit disc to the Bergman space of subdomains with large symmetry groups, such as horodiscs and subdomains bounded by hypercycles. Furthermore, we prove a sharp estimate of the norm of the restriction operator in case the domain and the subdomain are balls. We also study various operator theoretic properties of the restriction operator such as compactness and essential norm estimates. |
| doi_str_mv | 10.1007/s12220-019-00178-3 |
| format | Article |
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∂
¯
-Neumann operator, we study the restriction operator from the Bergman space of a domain in
C
n
to the Bergman space of a non-empty open subset of the domain. We relate the restriction operator to the Toeplitz operator on the Bergman space of the domain whose symbol is the characteristic function of the subset. Using the biholomorphic invariance of the spectrum of the associated Toeplitz operator, we study the restriction operator from the Bergman space of the unit disc to the Bergman space of subdomains with large symmetry groups, such as horodiscs and subdomains bounded by hypercycles. Furthermore, we prove a sharp estimate of the norm of the restriction operator in case the domain and the subdomain are balls. We also study various operator theoretic properties of the restriction operator such as compactness and essential norm estimates.</description><identifier>ISSN: 1050-6926</identifier><identifier>EISSN: 1559-002X</identifier><identifier>DOI: 10.1007/s12220-019-00178-3</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Abstract Harmonic Analysis ; Characteristic functions ; Convex and Discrete Geometry ; Differential Geometry ; Domains ; Dynamical Systems and Ergodic Theory ; Fourier Analysis ; Geometry ; Global Analysis and Analysis on Manifolds ; Mathematics ; Mathematics and Statistics</subject><ispartof>The Journal of Geometric Analysis, 2020-04, Vol.30 (2), p.2157-2188</ispartof><rights>Mathematica Josephina, Inc. 2019</rights><rights>COPYRIGHT 2020 Springer</rights><rights>2019© Mathematica Josephina, Inc. 2019</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c358t-9d7f8dd5613d8e36a9e88ec60ef0d04e1227020b47df5ce2bf4b5cea63c1d61e3</citedby><cites>FETCH-LOGICAL-c358t-9d7f8dd5613d8e36a9e88ec60ef0d04e1227020b47df5ce2bf4b5cea63c1d61e3</cites><orcidid>0000-0002-0473-8542</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s12220-019-00178-3$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s12220-019-00178-3$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Chakrabarti, Debraj</creatorcontrib><creatorcontrib>Şahutoğlu, Sönmez</creatorcontrib><title>The Restriction Operator on Bergman Spaces</title><title>The Journal of Geometric Analysis</title><addtitle>J Geom Anal</addtitle><description>Motivated by questions related to the compactness of the
∂
¯
-Neumann operator, we study the restriction operator from the Bergman space of a domain in
C
n
to the Bergman space of a non-empty open subset of the domain. We relate the restriction operator to the Toeplitz operator on the Bergman space of the domain whose symbol is the characteristic function of the subset. Using the biholomorphic invariance of the spectrum of the associated Toeplitz operator, we study the restriction operator from the Bergman space of the unit disc to the Bergman space of subdomains with large symmetry groups, such as horodiscs and subdomains bounded by hypercycles. Furthermore, we prove a sharp estimate of the norm of the restriction operator in case the domain and the subdomain are balls. We also study various operator theoretic properties of the restriction operator such as compactness and essential norm estimates.</description><subject>Abstract Harmonic Analysis</subject><subject>Characteristic functions</subject><subject>Convex and Discrete Geometry</subject><subject>Differential Geometry</subject><subject>Domains</subject><subject>Dynamical Systems and Ergodic Theory</subject><subject>Fourier Analysis</subject><subject>Geometry</subject><subject>Global Analysis and Analysis on Manifolds</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><issn>1050-6926</issn><issn>1559-002X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><recordid>eNp9kEFLAzEQhYMoWKt_wNOCN2HrJNlNssdarAqFglbwFtJkUre0u2uyPfjvTV3Bm8xhJsP7Jo9HyDWFCQWQd5EyxiAHWuUAVKqcn5ARLcvjk72fphlKyEXFxDm5iHELUAheyBG5XX1g9oKxD7Xt67bJlh0G07chS_M9hs3eNNlrZyzGS3LmzS7i1W8fk7f5w2r2lC-Wj8-z6SK3vFR9XjnplXOloNwp5MJUqBRaAejBQYHJqQQG60I6X1pka1-sUzeCW-oERT4mN8PdLrSfh2RNb9tDaNKXmnFVKAGSlUk1GVQbs0NdN77tg7GpHO5r2zbo67SfSpCcV5UQCWADYEMbY0Cvu1DvTfjSFPQxRD2EqFOI-idEzRPEBygmcbPB8OflH-obd9NzDA</recordid><startdate>20200401</startdate><enddate>20200401</enddate><creator>Chakrabarti, Debraj</creator><creator>Şahutoğlu, Sönmez</creator><general>Springer US</general><general>Springer</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>IAO</scope><orcidid>https://orcid.org/0000-0002-0473-8542</orcidid></search><sort><creationdate>20200401</creationdate><title>The Restriction Operator on Bergman Spaces</title><author>Chakrabarti, Debraj ; Şahutoğlu, Sönmez</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c358t-9d7f8dd5613d8e36a9e88ec60ef0d04e1227020b47df5ce2bf4b5cea63c1d61e3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Abstract Harmonic Analysis</topic><topic>Characteristic functions</topic><topic>Convex and Discrete Geometry</topic><topic>Differential Geometry</topic><topic>Domains</topic><topic>Dynamical Systems and Ergodic Theory</topic><topic>Fourier Analysis</topic><topic>Geometry</topic><topic>Global Analysis and Analysis on Manifolds</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Chakrabarti, Debraj</creatorcontrib><creatorcontrib>Şahutoğlu, Sönmez</creatorcontrib><collection>CrossRef</collection><collection>Gale Academic OneFile</collection><jtitle>The Journal of Geometric Analysis</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Chakrabarti, Debraj</au><au>Şahutoğlu, Sönmez</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The Restriction Operator on Bergman Spaces</atitle><jtitle>The Journal of Geometric Analysis</jtitle><stitle>J Geom Anal</stitle><date>2020-04-01</date><risdate>2020</risdate><volume>30</volume><issue>2</issue><spage>2157</spage><epage>2188</epage><pages>2157-2188</pages><issn>1050-6926</issn><eissn>1559-002X</eissn><abstract>Motivated by questions related to the compactness of the
∂
¯
-Neumann operator, we study the restriction operator from the Bergman space of a domain in
C
n
to the Bergman space of a non-empty open subset of the domain. We relate the restriction operator to the Toeplitz operator on the Bergman space of the domain whose symbol is the characteristic function of the subset. Using the biholomorphic invariance of the spectrum of the associated Toeplitz operator, we study the restriction operator from the Bergman space of the unit disc to the Bergman space of subdomains with large symmetry groups, such as horodiscs and subdomains bounded by hypercycles. Furthermore, we prove a sharp estimate of the norm of the restriction operator in case the domain and the subdomain are balls. We also study various operator theoretic properties of the restriction operator such as compactness and essential norm estimates.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s12220-019-00178-3</doi><tpages>32</tpages><orcidid>https://orcid.org/0000-0002-0473-8542</orcidid></addata></record> |
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| issn | 1050-6926 1559-002X |
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| subjects | Abstract Harmonic Analysis Characteristic functions Convex and Discrete Geometry Differential Geometry Domains Dynamical Systems and Ergodic Theory Fourier Analysis Geometry Global Analysis and Analysis on Manifolds Mathematics Mathematics and Statistics |
| title | The Restriction Operator on Bergman Spaces |
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