Weighted Composition Operators from Hardy Spaces into Logarithmic Bloch Spaces
The logarithmic Bloch space Blog is the Banach space of analytic functions on the open unit disk 𝔻 whose elements f satisfy the condition ∥f∥=supz∈𝔻(1-|z|2)log (2/(1-|z|2))|f'(z)|<∞. In this work we characterize the bounded and the compact weighted composition ope...
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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/10.1155/2012/454820 |
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| _version_ | 1832562095362670592 |
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| author | Flavia Colonna Songxiao Li |
| author_facet | Flavia Colonna Songxiao Li |
| author_sort | Flavia Colonna |
| collection | DOAJ |
| description | The logarithmic Bloch space Blog is the Banach space of analytic functions on the open unit disk 𝔻 whose elements f satisfy the condition ∥f∥=supz∈𝔻(1-|z|2)log (2/(1-|z|2))|f'(z)|<∞. In this work we characterize the bounded and the compact weighted composition operators from the Hardy space Hp (with 1≤p≤∞) into the logarithmic Bloch space. We also provide boundedness and compactness criteria for the weighted composition operator mapping Hp into the little logarithmic Bloch space defined as the subspace of Blog consisting of the functions f such that lim|z|→1(1-|z|2)log (2/(1-|z|2))|f'(z)|=0. |
| format | Article |
| id | doaj-art-04587c9bfe004b92950acd7947f2ed33 |
| 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-04587c9bfe004b92950acd7947f2ed332025-02-03T01:23:27ZengWileyJournal of Function Spaces and Applications0972-68021758-49652012-01-01201210.1155/2012/454820454820Weighted Composition Operators from Hardy Spaces into Logarithmic Bloch SpacesFlavia Colonna0Songxiao Li1Department of Mathematical Sciences, George Mason University, Fairfax, VA 22030, USADepartment of Mathematics, Jiaying University, Guangdong, Meizhou 514015, ChinaThe logarithmic Bloch space Blog is the Banach space of analytic functions on the open unit disk 𝔻 whose elements f satisfy the condition ∥f∥=supz∈𝔻(1-|z|2)log (2/(1-|z|2))|f'(z)|<∞. In this work we characterize the bounded and the compact weighted composition operators from the Hardy space Hp (with 1≤p≤∞) into the logarithmic Bloch space. We also provide boundedness and compactness criteria for the weighted composition operator mapping Hp into the little logarithmic Bloch space defined as the subspace of Blog consisting of the functions f such that lim|z|→1(1-|z|2)log (2/(1-|z|2))|f'(z)|=0.http://dx.doi.org/10.1155/2012/454820 |
| spellingShingle | Flavia Colonna Songxiao Li Weighted Composition Operators from Hardy Spaces into Logarithmic Bloch Spaces Journal of Function Spaces and Applications |
| title | Weighted Composition Operators from Hardy Spaces into Logarithmic Bloch Spaces |
| title_full | Weighted Composition Operators from Hardy Spaces into Logarithmic Bloch Spaces |
| title_fullStr | Weighted Composition Operators from Hardy Spaces into Logarithmic Bloch Spaces |
| title_full_unstemmed | Weighted Composition Operators from Hardy Spaces into Logarithmic Bloch Spaces |
| title_short | Weighted Composition Operators from Hardy Spaces into Logarithmic Bloch Spaces |
| title_sort | weighted composition operators from hardy spaces into logarithmic bloch spaces |
| url | http://dx.doi.org/10.1155/2012/454820 |
| work_keys_str_mv | AT flaviacolonna weightedcompositionoperatorsfromhardyspacesintologarithmicblochspaces AT songxiaoli weightedcompositionoperatorsfromhardyspacesintologarithmicblochspaces |