Maximal functions: Poisson integrals on symmetric spaces | Zendy

Elias M. Stein | Zendy

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Maximal functions: Poisson integrals on symmetric spaces

Author(s) -

Elias M. Stein

Publication year - 1976

Publication title -

proceedings of the national academy of sciences

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.

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