Existence of Extremals of Dunkl-Type Sobolev Inequality and of Stein–Weiss Inequality for Dunkl Riesz Potential

被引：0
作者：
Saswata Adhikari
V. P. Anoop
Sanjay Parui
机构：
[1] NISER Bhubaneswar,School of Mathematical Sciences
[2] Homi Bhabha National Institute,Department of Mathematics
[3] SRM University-AP,Department of Mathematics
[4] Indian Institute of Science,undefined
来源：
Complex Analysis and Operator Theory | 2021年 / 15卷
关键词：
Dunkl transform; Riesz potential; Sobolev inequality; Stein–Weiss inequality; Primary 42B10; Secondary 33C52; 35R11; 35A23;
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摘要：
In this paper, we prove the existence of an extremal for the Dunkl-type Sobolev inequality in the case of p=2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p=2$$\end{document}. Also we prove the existence of an extremal of the Stein–Weiss inequality for the Dunkl Riesz potential in the case of r=2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$r=2$$\end{document}.
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