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...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
|
| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2012/454820 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | 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. |
|---|---|
| ISSN: | 0972-6802 1758-4965 |