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- Title
Estimates for singular numbers of Hausdorff–Zhu operators and applications.
- Authors
Grudsky, Sergei; Karapetyants, Alexey; Mirotin, Adolf
- Abstract
We continue the study of the so‐called Hausdorff–Zhu operators. In this paper, we study the behavior of the singular values of such operators. We prove the general fact that the sequence of singular numbers tends to zero, as well as we prove power‐type estimates for such behavior under additional conditions on the kernel of the operator. We give application of these results to the boundedness of Hausdorff–Zhu operators in general classes of analytic functions in the unit disc and also in some special classes of analytic functions defined in terms of conditions on Taylor or Fourier coefficients.
- Subjects
HARDY spaces; BERGMAN spaces; VALUES (Ethics); COMPOSITION operators; INTEGRAL operators; ANALYTIC functions
- Publication
Mathematical Methods in the Applied Sciences, 2023, Vol 46, Issue 8, p9676
- ISSN
0170-4214
- Publication type
Article
- DOI
10.1002/mma.9080