Some New Thoughts on Maximal Functions and Poisson Integrals

Details Some New Thoughts on Maximal Functions and Poisson Integrals Some New Thoughts on Maximal Functions and Poisson Integrals

2010-10-06

arxiv.org/abs/1010.1270v1

Mathematics

Analysis of PDEs

no figures

Scientific paper

We study Wiener-type covering lemmas, Hardy-Littlewood-type maximal
functions, and convergence theorems on metric spacs. Later we specialize down
to a result for the Poisson integral. We show that, in a suitably general
setting, these three phenomena are essentially logically equivalent. Along the
way we discuss some useful estimates for the Poisson kernel.

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