Open AccessMaximal functions: Poisson integrals on symmetric spaces
Author(s) -
Elias M. Stein
Publication year - 1976
Publication title -
proceedings of the national academy of sciences of the united states of america
Language(s) - English
Resource type - Journals
eISSN - 1091-6490
pISSN - 0027-8424
DOI - 10.1073/pnas.73.8.2547
Subject(s) - poisson kernel , poisson distribution , mathematics , infinity , kernel (algebra) , function (biology) , harmonic function , space (punctuation) , mathematical analysis , pure mathematics , uniqueness theorem for poisson's equation , computer science , statistics , uniqueness , evolutionary biology , biology , operating system
Letu be a harmonic function on a symmetric space which is the Poisson integral of a functionf inLp , 1 ≤p ≤ ∞. Thenu converges restrictedly and admissibly tof almost everywhere. This result is proved by obtaining an appropriate maximal theorem which takes into account the structure of the Poisson kernel.