On maximal functions and Poisson-Szegő integrals

Sueiro, Juan

doi:10.1090/S0002-9947-1986-0860386-8

On maximal functions and Poisson-Szegő integrals
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Trans. Amer. Math. Soc. 298 (1986), 653-669 Request permission

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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