Sharp Estimates for Potential Operators Associated with Laguerre and Dunkl-Laguerre Expansions

被引：5

作者：

Nowak, Adam ^{[1
]}

Stempak, Krzysztof ^{[2
]}

机构：

[1] Polish Acad Sci, Inst Matematyczny, Sniadeckich 8, PL-00656 Warsaw, Poland

[2] Wroclaw Univ Technol, Wydzial Matematyki, Wyb Wyspianskiego 27, PL-50370 Wroclaw, Poland

来源：

POTENTIAL ANALYSIS | 2016年 / 44卷 / 01期

关键词：

Laguerre expansion; Dunkl-Laguerre expansion; Laguerre operator; Dunkl harmonic oscillator; Negative power; Potential operator; Fractional integral; Potential kernel; SPACES;

D O I：

10.1007/s11118-015-9501-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study potential operators associated with Laguerre function expansions of convolution and Hermite types, and with Dunkl-Laguerre expansions. We prove qualitatively sharp estimates of the corresponding potential kernels. Then we characterize those 1 a parts per thousand currency sign p,q a parts per thousand currency sign 8, for which the potential operators are L (p) - L (q) bounded. These results are sharp analogues of the classical Hardy-Littlewood-Sobolev fractional integration theorem in the Laguerre and Dunkl-Laguerre settings.

引用

页码：109 / 136

页数：28

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