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.
Stein
E M
EM
Department of Mathematics, Princeton University, Princeton, New Jersey 08540.