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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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). |
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| ISSN: | 0972-6802 1758-4965 |