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Small Bergman-Orlicz and Hardy-Orlicz spaces, and their composition operators
We show that the weighted Bergman-Orlicz space A α ψ coincides with some weighted Banach space of holomorphic functions if and only if the Orlicz function ψ satisfies the so-called Δ 2 -condition. In addition we prove that this condition characterizes those A α ψ on which every composition operator...
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| Published in: | Mathematische Zeitschrift 2019-12, Vol.293 (3-4), p.1287-1314 |
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| Format: | Article |
| Language: | English |
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| container_title | Mathematische Zeitschrift |
| container_volume | 293 |
| creator | Charpentier, S. |
| description | We show that the weighted Bergman-Orlicz space
A
α
ψ
coincides with some weighted Banach space of holomorphic functions if and only if the Orlicz function
ψ
satisfies the so-called
Δ
2
-condition. In addition we prove that this condition characterizes those
A
α
ψ
on which every composition operator is bounded or order bounded into the Orlicz space
L
α
ψ
. This provides us with estimates of the norm and the essential norm of composition operators on such spaces. We also prove that when
ψ
satisfies the
Δ
2
-condition, a composition operator is compact on
A
α
ψ
if and only if it is order bounded into the so-called Morse–Transue space
M
α
ψ
. Our results stand in the unit ball of
C
N
. |
| doi_str_mv | 10.1007/s00209-019-02240-w |
| format | article |
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A
α
ψ
coincides with some weighted Banach space of holomorphic functions if and only if the Orlicz function
ψ
satisfies the so-called
Δ
2
-condition. In addition we prove that this condition characterizes those
A
α
ψ
on which every composition operator is bounded or order bounded into the Orlicz space
L
α
ψ
. This provides us with estimates of the norm and the essential norm of composition operators on such spaces. We also prove that when
ψ
satisfies the
Δ
2
-condition, a composition operator is compact on
A
α
ψ
if and only if it is order bounded into the so-called Morse–Transue space
M
α
ψ
. Our results stand in the unit ball of
C
N
.</description><identifier>ISSN: 0025-5874</identifier><identifier>EISSN: 1432-1823</identifier><identifier>DOI: 10.1007/s00209-019-02240-w</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Analytic functions ; Banach spaces ; Composition ; Mathematics ; Mathematics and Statistics ; Operators (mathematics) ; Orlicz space</subject><ispartof>Mathematische Zeitschrift, 2019-12, Vol.293 (3-4), p.1287-1314</ispartof><rights>Springer-Verlag GmbH Germany, part of Springer Nature 2019</rights><rights>Copyright Springer Nature B.V. 2019</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c319t-66777d8efbb433b939c097656dcf8af1c3be2c3ad463041e393f7372b2b816f03</citedby><cites>FETCH-LOGICAL-c319t-66777d8efbb433b939c097656dcf8af1c3be2c3ad463041e393f7372b2b816f03</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><creatorcontrib>Charpentier, S.</creatorcontrib><title>Small Bergman-Orlicz and Hardy-Orlicz spaces, and their composition operators</title><title>Mathematische Zeitschrift</title><addtitle>Math. Z</addtitle><description>We show that the weighted Bergman-Orlicz space
A
α
ψ
coincides with some weighted Banach space of holomorphic functions if and only if the Orlicz function
ψ
satisfies the so-called
Δ
2
-condition. In addition we prove that this condition characterizes those
A
α
ψ
on which every composition operator is bounded or order bounded into the Orlicz space
L
α
ψ
. This provides us with estimates of the norm and the essential norm of composition operators on such spaces. We also prove that when
ψ
satisfies the
Δ
2
-condition, a composition operator is compact on
A
α
ψ
if and only if it is order bounded into the so-called Morse–Transue space
M
α
ψ
. Our results stand in the unit ball of
C
N
.</description><subject>Analytic functions</subject><subject>Banach spaces</subject><subject>Composition</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Operators (mathematics)</subject><subject>Orlicz space</subject><issn>0025-5874</issn><issn>1432-1823</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><recordid>eNp9kEFPwzAMhSMEEmPwBzhV4krAibumOcIEDGloB-AcpWk6OrVNSTqh8esJK4gbB8uS33u2_BFyzuCKAYjrAMBBUmCxOE-BfhyQCUuRU5ZzPCSTqM_oLBfpMTkJYQMQRZFOyNNzq5smubV-3eqOrnxTm89Ed2Wy0L7c_Q5Cr40Nl3theLO1T4xrexfqoXZd4nrr9eB8OCVHlW6CPfvpU_J6f_cyX9Dl6uFxfrOkBpkcaJYJIcrcVkWRIhYSpQEpsllWmirXFTNYWG5Ql2mGkDKLEiuBghe8yFlWAU7Jxbi39-59a8OgNm7ru3hScQQpWR7fjS4-uox3IXhbqd7XrfY7xUB9Y1MjNhWxqT029RFDOIZCNHdr6_9W_5P6AmKPcBA</recordid><startdate>20191201</startdate><enddate>20191201</enddate><creator>Charpentier, S.</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20191201</creationdate><title>Small Bergman-Orlicz and Hardy-Orlicz spaces, and their composition operators</title><author>Charpentier, S.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-66777d8efbb433b939c097656dcf8af1c3be2c3ad463041e393f7372b2b816f03</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Analytic functions</topic><topic>Banach spaces</topic><topic>Composition</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Operators (mathematics)</topic><topic>Orlicz space</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Charpentier, S.</creatorcontrib><collection>CrossRef</collection><jtitle>Mathematische Zeitschrift</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Charpentier, S.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Small Bergman-Orlicz and Hardy-Orlicz spaces, and their composition operators</atitle><jtitle>Mathematische Zeitschrift</jtitle><stitle>Math. Z</stitle><date>2019-12-01</date><risdate>2019</risdate><volume>293</volume><issue>3-4</issue><spage>1287</spage><epage>1314</epage><pages>1287-1314</pages><issn>0025-5874</issn><eissn>1432-1823</eissn><abstract>We show that the weighted Bergman-Orlicz space
A
α
ψ
coincides with some weighted Banach space of holomorphic functions if and only if the Orlicz function
ψ
satisfies the so-called
Δ
2
-condition. In addition we prove that this condition characterizes those
A
α
ψ
on which every composition operator is bounded or order bounded into the Orlicz space
L
α
ψ
. This provides us with estimates of the norm and the essential norm of composition operators on such spaces. We also prove that when
ψ
satisfies the
Δ
2
-condition, a composition operator is compact on
A
α
ψ
if and only if it is order bounded into the so-called Morse–Transue space
M
α
ψ
. Our results stand in the unit ball of
C
N
.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s00209-019-02240-w</doi><tpages>28</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0025-5874 |
| ispartof | Mathematische Zeitschrift, 2019-12, Vol.293 (3-4), p.1287-1314 |
| issn | 0025-5874 1432-1823 |
| language | eng |
| recordid | cdi_proquest_journals_2309918025 |
| source | Springer Nature |
| subjects | Analytic functions Banach spaces Composition Mathematics Mathematics and Statistics Operators (mathematics) Orlicz space |
| title | Small Bergman-Orlicz and Hardy-Orlicz spaces, and their composition operators |
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