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On maximal functions and Poisson-Szegö integrals. (English) Zbl 0612.32007
The paper is concerned with the maximal function \(M_{\Omega}f\) defined on spaces of homogeneous type X. The necessary and sufficient conditions on the family \(\{\Omega_ t, t\in X\}\) for \(M_{\Omega}\) to be of weak type (1,1) are given. The author applies these to study boundary limits of Poisson-Szegö integrals on the generalized half-plane and on the unit ball of \({\mathbb{C}}^ n\).
Reviewer: A.Zabulionis

MSC:
32A40 Boundary behavior of holomorphic functions of several complex variables
42B25 Maximal functions, Littlewood-Paley theory
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