Maximal functions associated to smooth curves.
Let t --> gamma(t), 0 </= t </= 1, be a smooth curve in IR(n). Define the maximal function [unk](f) by [unk](f)(x) = sup(0<h</=1) (1/h) (0) (h) f(x - gamma(t)) dt. We state conditions under which parallel[unk](f) parallel(p) </= A(p) parallelf parallel(p), for 1 < p </= infinity.
Department of Mathematics, Princeton University, Princeton, New Jersey. 08540.
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Stein
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Wainger