Estimates for singular numbers of Hausdorff–Zhu operators and applications

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.