Fourier Multipliers in Hardy Spaces in Tubes over Open Cones

被引：1
|
作者：
Tovstolis, Alexander V. [1 ]
机构：
[1] Oklahoma State Univ, Dept Math, Stillwater, OK 74078 USA
来源：
COMPUTATIONAL METHODS AND FUNCTION THEORY | 2014年 / 14卷 / 04期
关键词：
Fourier multiplier; Hardy spaces in tubes over open cones; Fourier integral; Multiplier defined by a radial function; Bochner-Riesz means; Nikol'skij type inequality; Non-increasing rearrangement;
D O I：
10.1007/s40315-014-0079-6
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We obtain effective sufficient conditions for multipliers of Fourier integrals acting from H-p (T-Gamma) to H-q (T-Gamma), 0 < p <= q <= 1. We also show that they are sharp in some cases. Special attention is paid to the means of Fourier integrals with compactly supported radial kernels. As an application, the critical index for the Bochner-Riesz means to define a bounded linear operator from H-p to H-q is found. Surprisingly, it does not depend on p.
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页码：681 / 719
页数：39
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