Biomedical subjects
Publications and source records attributed to S Wainger.
We study several notions of distance and ball on the boundary of domains of finite type in C(n). We use these notions to develop a theory of maximal functions and area integrals for functions holomorphic in such domains.
Let {theta(j)} be a lacunary sequence going to zero. Let [Formula: see text]. Define [Formula: see text]. We prove [Formula: see text].
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.
THE AUTHORS PROVE THAT [FORMULA: see text] is bounded from L(P)(R(2)) to L(P)(R(2)) for 1 < p </= infinity.