Maximal functions: Spherical means.
Let [unk](f)(x) denote the supremum of the averages of f taken over all (surfaces of) spheres centered at x. Then f --> [unk](f) is bounded on L(p)(R(n)), whenever p > n/(n - 1), and n >/= 3.
Stein
E M
EM
Department of Mathematics, Princeton University, Princeton, New Jersey 08540.