Sharp weighted convolution inequalities and some applications

被引：12

作者：

Guo, Weichao ^{[1
]}

Fan, Dashan ^{[2
]}

Wu, Huoxiong ^{[3
]}

Zhao, Guoping ^{[4
]}

机构：

[1] Guangzhou Univ, Sch Math & Informat Sci, Guangzhou 510006, Guangdong, Peoples R China

[2] Univ Wisconsin, Dept Math, Milwaukee, WI 53201 USA

[3] Xiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China

[4] Xiamen Univ Technol, Sch Appl Math, Xiamen 361024, Peoples R China

来源：

STUDIA MATHEMATICA | 2018年 / 241卷 / 03期

基金：

中国博士后科学基金;

关键词：

weighted convolution inequalities; fractional integrals; discrete analogue; characterization; modulation spaces; NAVIER-STOKES EQUATIONS; FRACTIONAL INTEGRALS; MODULATION SPACES; FOURIER MULTIPLIERS; NORM INEQUALITIES; RADIAL FUNCTIONS; TRANSFORMS; OPERATORS; THEOREMS;

D O I：

10.4064/sm8583-5-2017

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The index groups for which weighted Young inequalities hold in both the continuous case and discrete case are characterized. As applications, the index groups for the product inequalities on modulation spaces are characterized, and we also obtain the weakest conditions for the boundedness of bilinear Fourier multipliers on modulation spaces. For the fractional integral operator, sharp conditions for the power weighted L-p - L-q estimates in both the continuous and discrete cases are obtained. By a novel unified approach, we complete some previous results on sharp conditions for some classical inequalities.

引用

页码：201 / 239

页数：39

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