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Integration operators in average radial integrability spaces of analytic functions. (English) Zbl 1468.30092

Summary: In this paper we characterize the boundedness, compactness, and weak compactness of the integration operators \[ T_g (f)(z)=\int_0^z f(w)g'(w) dw \] 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.

MSC:

30H20 Bergman spaces and Fock spaces
30H10 Hardy spaces
47G10 Integral operators
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