Bochner-Riesz Means of Morrey Functions

This paper concerns both norm estimation and pointwise approximation for the Bochner-Riesz means of an arbitrary Morrey function on R-n-Theorems 1.1 and 1.2 for L-p,L-lambda(R-n)-thereby generalizing the corresponding results for L-p(R-n) in Stein (Acta Math 100:93-147, 1958) and Carbery et al. (J Lond Math Soc 38:513-524, 1988). As a side note, this paper also establishes Lemma 4.1 of Tomas-Stein type-if f is an element of L-p,L-lambda(R-n) under 2(-1)(n + 1) < lambda = n is compactly supported, then parallel to<(f)over cap>parallel to(L2(Sn-1)) less than or similar to parallel to f parallel to(Lp,lambda(Rn)) for 4 lambda/n + 1 + 2 lambda <= p < 2 lambda/n + 1.