Integration operators in average radial integrability spaces of analytic functions
Functional Analysis
2020-05-25 v1
Abstract
In this paper we characterize the boundedness, compactness, and weak compactness of the integration operators \begin{align*} T_g (f)(z)=\int_{0}^{z} f(w)g'(w)\ dw \end{align*} acting on the average radial integrability spaces . For these purposes, we develop different tools such as a description of the bidual of and estimates of the norm of these spaces using the derivative of the functions, a family of results that we call Littlewood-Paley type inequalities.
Keywords
Cite
@article{arxiv.2005.10909,
title = {Integration operators in average radial integrability spaces of analytic functions},
author = {Tanausú Aguilar-Hernández and Manuel D. Contreras and Luis Rodríguez-Piazza},
journal= {arXiv preprint arXiv:2005.10909},
year = {2020}
}