Integration Operators in Average Radial Integrability Spaces of Analytic Functions

Abstract

In this paper we characterize the boundedness, compactness, and weak compactness of the integration operators $$\begin{aligned} T_g (f)(z)=\int _{0}^{z} f(w)g'(w)\ dw \end{aligned}$$ acting on the average radial integrability spaces RM(p, q). For these purposes, we develop different tools such as a description of the bidual of 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.