Weighted composition operators from Banach spaces of analytic functions into Bloch-type spaces. (English) Zbl 1369.47026
Botelho, Fernanda (ed.) et al., Problems and recent methods in operator theory. Workshop on problems and recent methods in operator theory, University of Memphis, Memphis, TN, USA, October 15–16, 2015 and AMS special session on advances in operator theory and applications, University of Memphis, Memphis, TN, USA, October 17–18, 2015. Proceedings dedicated to the memory of Professor James E. Jamison. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-2772-6/pbk; 978-1-4704-4040-4/ebook). Contemporary Mathematics 687, 75-95 (2017).
Summary: In this work, we characterize boundedness and compactness of weighted composition operators from the class of Banach space of analytic functions that are continuously contained in the Bloch space and such that the disk automorphisms have bounded norm, into Bloch-type spaces. We apply our results to several spaces, including the Bloch space, the analytic Besov spaces, and the space of analytic functions of bounded mean oscillation. We also obtain boundedness and compactness criteria for such operators when the domain is the space \(S^p\) of the analytic functions on the unit disk whose derivative is in the Hardy space \(H^p\) for \(p\geq 1\).
For the entire collection see [Zbl 1366.46002].
For the entire collection see [Zbl 1366.46002].
MSC:
| 47B33 | Linear composition operators |
| 47B38 | Linear operators on function spaces (general) |
| 30H05 | Spaces of bounded analytic functions of one complex variable |
| 46E22 | Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) |
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