Maximal functions: Poisson integrals on symmetric spaces.
Let u be a harmonic function on a symmetric space which is the Poisson integral of a function f in L(p), 1 </= p </= infinity. Then u converges restrictedly and admissibly to f almost everywhere. This result is proved by obtaining an appropriate maximal theorem which takes into account the structure of the Poisson kernel.
Department of Mathematics, Princeton University, Princeton, New Jersey 08540.
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Stein