Integration operators on Hardy and Bergman spaces

TL;DR

This paper investigates the properties of compact integration operators on Hardy and Bergman spaces, providing estimates for their singular values to understand their behavior and boundedness.

Contribution

It offers new bounds for the singular values of integration operators on Hardy and weighted Bergman spaces, advancing the understanding of their compactness and spectral properties.

Findings

Derived upper and lower estimates for singular values

Characterized compactness criteria for the operators

Enhanced understanding of operator behavior on function spaces

Abstract

In the present work, we are interested in compact integration operators $I_g f(z) = \int_0^z f(\zeta)g'(\zeta)d\zeta$ acting on the Hardy space $H^2$ and on the weighted Bergman spaces $\mathcal{A}^2_\alpha$. We give upper and lower estimates for the singular values of $I_g$.