Carleson Measure Theorems for Large Hardy-Orlicz and Bergman-Orlicz Spaces
We characterize those measures μ for which the Hardy-Orlicz (resp., weighted Bergman-Orlicz) space HΨ1 (resp., AαΨ1) of the unit ball of CN embeds boundedly or compactly into the Orlicz space LΨ2(BN¯,μ) (resp., LΨ2(BN,μ)), when the defining functions Ψ1 and Ψ2 are growth functions such that L1⊂LΨj f...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2012/792763 |
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| author | Stéphane Charpentier Benoît Sehba |
| author_facet | Stéphane Charpentier Benoît Sehba |
| author_sort | Stéphane Charpentier |
| collection | DOAJ |
| description | We characterize those measures μ for which the Hardy-Orlicz (resp., weighted Bergman-Orlicz) space HΨ1 (resp., AαΨ1) of the unit ball of CN embeds boundedly or compactly into the Orlicz space LΨ2(BN¯,μ) (resp., LΨ2(BN,μ)), when the defining functions Ψ1 and Ψ2 are growth functions such that L1⊂LΨj for j∈{1,2}, and such that Ψ2/Ψ1 is nondecreasing. We apply our result to the characterization of the boundedness and compactness of composition operators from HΨ1 (resp., AαΨ1) into HΨ2 (resp., AαΨ2). |
| format | Article |
| id | doaj-art-2de17b8d738c400299d0c8cf8368b357 |
| institution | Kabale University |
| issn | 0972-6802 1758-4965 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-2de17b8d738c400299d0c8cf8368b3572025-02-03T07:26:14ZengWileyJournal of Function Spaces and Applications0972-68021758-49652012-01-01201210.1155/2012/792763792763Carleson Measure Theorems for Large Hardy-Orlicz and Bergman-Orlicz SpacesStéphane Charpentier0Benoît Sehba1Département de Mathématiques, Université Paris-Sud, Bâtiment 425, 91405 Orsay, FranceSchool of Mathematics, Trinity College, Dublin 2, IrelandWe characterize those measures μ for which the Hardy-Orlicz (resp., weighted Bergman-Orlicz) space HΨ1 (resp., AαΨ1) of the unit ball of CN embeds boundedly or compactly into the Orlicz space LΨ2(BN¯,μ) (resp., LΨ2(BN,μ)), when the defining functions Ψ1 and Ψ2 are growth functions such that L1⊂LΨj for j∈{1,2}, and such that Ψ2/Ψ1 is nondecreasing. We apply our result to the characterization of the boundedness and compactness of composition operators from HΨ1 (resp., AαΨ1) into HΨ2 (resp., AαΨ2).http://dx.doi.org/10.1155/2012/792763 |
| spellingShingle | Stéphane Charpentier Benoît Sehba Carleson Measure Theorems for Large Hardy-Orlicz and Bergman-Orlicz Spaces Journal of Function Spaces and Applications |
| title | Carleson Measure Theorems for Large Hardy-Orlicz and Bergman-Orlicz Spaces |
| title_full | Carleson Measure Theorems for Large Hardy-Orlicz and Bergman-Orlicz Spaces |
| title_fullStr | Carleson Measure Theorems for Large Hardy-Orlicz and Bergman-Orlicz Spaces |
| title_full_unstemmed | Carleson Measure Theorems for Large Hardy-Orlicz and Bergman-Orlicz Spaces |
| title_short | Carleson Measure Theorems for Large Hardy-Orlicz and Bergman-Orlicz Spaces |
| title_sort | carleson measure theorems for large hardy orlicz and bergman orlicz spaces |
| url | http://dx.doi.org/10.1155/2012/792763 |
| work_keys_str_mv | AT stephanecharpentier carlesonmeasuretheoremsforlargehardyorliczandbergmanorliczspaces AT benoitsehba carlesonmeasuretheoremsforlargehardyorliczandbergmanorliczspaces |