Estimates for singular numbers of Hausdorff–Zhu operators and applications
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 co...
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| Veröffentlicht in: | Mathematical methods in the applied sciences 2023-05, Vol.46 (8), p.9676-9693 |
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| container_title | Mathematical methods in the applied sciences |
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| creator | Grudsky, Sergei Karapetyants, Alexey Mirotin, Adolf |
| description | 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. |
| doi_str_mv | 10.1002/mma.9080 |
| format | Article |
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| ispartof | Mathematical methods in the applied sciences, 2023-05, Vol.46 (8), p.9676-9693 |
| issn | 0170-4214 1099-1476 |
| language | eng |
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| source | Wiley Online Library Journals Frontfile Complete |
| subjects | Analytic functions Bergman and Hardy spaces Estimates Hausdorff operator Hausdorff–Zhu operator integral operator Mathematical analysis Operators |
| title | Estimates for singular numbers of Hausdorff–Zhu operators and applications |
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