Riesz Transform Characterizations for Multidimensional Hardy Spaces

被引：0
作者：
Edyta Kania-Strojec
Marcin Preisner
机构：
[1] Uniwersytet Wrocławski,Instytut Matematyczny
来源：
The Journal of Geometric Analysis | 2022年 / 32卷
关键词：
Hardy space; Riesz transform; Bessel operator; Laguerre operator; Dirichlet Laplacian; Primary 42B30; Secondary 42B20; 42B25; 33C45;
D O I：
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学科分类号：
摘要：
We study Hardy space HL1(X)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H^1_L(X)$$\end{document} related to a self-adjoint operator L defined on an Euclidean subspace X of Rd\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathbb {R}}^d}$$\end{document}. We continue study from [27], where, under certain assumptions on the heat semigroup exp(-tL)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\exp (-tL)$$\end{document}, the atomic characterization of local type for HL1(X)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H^1_L(X)$$\end{document} was proved. In this paper we provide additional assumptions that lead to another characterization of HL1(X)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H^1_L(X)$$\end{document} by the Riesz transforms related to L. As an application, we prove the Riesz transform characterization of HL1(X)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H^1_L(X)$$\end{document} for multidimensional Bessel and Laguerre operators, and the Dirichlet Laplacian on R+d\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {R}}^d_+$$\end{document}.
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