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,λ(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∈ L^p,λ(ℝ^n) under 2^-1(n+1)<λ≤ n is compactly supported, then ‖f̂‖ _L^2(𝕊^n-1)≲‖ f‖ _L^p,λ(ℝ^n) for 4λ/n+1+2λ≤ p<2λ/n+1.