Integration Operators in Average Radial Integrability Spaces of Analytic Functions

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