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arXiv · 2005.10909

Integration operators in average radial integrability spaces of analytic functions

Tanausú Aguilar-Hernández·Manuel D. Contreras·Luis Rodríguez-Piazza
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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 $RM(p,q)$. 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.

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BibTeXRIS

Tanausú Aguilar-Hernández, Manuel D. Contreras, Luis Rodríguez-Piazza. 2020-05-21. Integration operators in average radial integrability spaces of analytic functions. https://arxiv.org/abs/2005.10909

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