English

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 RM(p,q)RM(p,q). For these purposes, we develop different tools such as a description of the bidual of RM(p,0)RM(p,0) 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}
}
R2 v1 2026-06-23T15:43:41.068Z