Bochner-Riesz Means of Morrey Functions

被引：3
|
作者：
Adams, David R. [1 ]
Xiao, Jie [2 ]
机构：
[1] Univ Kentucky, Dept Math, Lexington, KY 40506 USA
[2] Mem Univ, Dept Math & Stat, St John, NF A1C 5S7, Canada
来源：
JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS | 2020年 / 26卷 / 01期
基金：
加拿大自然科学与工程研究理事会;
关键词：
Bochner-Riesz means; Fourier transforms; Morrey functions; WEIGHTED NORM INEQUALITIES; OSCILLATORY INTEGRALS; FOURIER; SPACES; SUMMABILITY; MULTIPLIERS;
D O I：
10.1007/s00041-019-09712-x
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
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页数：14
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