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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

On maximal functions and Poisson-Szegő integrals


Author: Juan Sueiro
Journal: Trans. Amer. Math. Soc. 298 (1986), 653-669
MSC: Primary 42B25; Secondary 32A40, 32M10
MathSciNet review: 860386
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Abstract: We study a class of maximal functions of Hardy-Littlewood type defined on spaces of homogeneous type and we give necessary and sufficient conditions for the corresponding maximal operators to be of weak type $ (1,1)$. As a consequence we show that Poisson-Szegö integrals of $ {L^p}$ functions possess certain boundary limits which are not implied by Korányi's theorem.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1986-0860386-8
PII: S 0002-9947(1986)0860386-8
Article copyright: © Copyright 1986 American Mathematical Society