Hardy spaces associated to generalized Hardy operators and applications

被引：0
作者：
The Anh Bui
Georges Nader
机构：
[1] Macquarie University,School of Mathematical and Physical Sciences
来源：
Nonlinear Differential Equations and Applications NoDEA | 2022年 / 29卷
关键词：
Generalized Hardy operator; Heat kernel; Hardy space; BMO space; Primary 35J10; Secondary 32A37; 30H10;
D O I：
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摘要：
In this paper, we will study the Hardy and BMO spaces associated to the generalized Hardy operator Lα=(-Δ)α/2+a|x|-α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_{\alpha }= (-\Delta )^{\alpha /2}+a|x|^{-\alpha }$$\end{document}. Similarly to the classical Hardy and BMO spaces, we will prove that our new function spaces will enjoy some important results such as molecular decomposition and duality. As applications, we show the boundedness of the spectral multiplier of Laplace transform type and the Sobolev norm inequalities involving the generalized Hardy operator.
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