Characterizations for the fractional maximal operator and its commutators in generalized weighted Morrey spaces on Carnot groups

被引：0
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作者：
V. S. Guliyev
机构：
[1] Baku State University,Institute of Applied Mathematics
[2] Dumlupinar University,Department of Mathematics
[3] RUDN University,S.M. Nikolskii Institute of Mathematics
来源：
Analysis and Mathematical Physics | 2020年 / 10卷
关键词：
Carnot group; Fractional maximal operator; Generalized weighted Morrey space; Commutator; Homogeneous dimension; Primary 42B25; 42B35; 43A15; 43A80;
D O I：
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摘要：
In this paper, we shall give a characterization for the strong and weak type Spanne type boundedness of the fractional maximal operator Mα\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$M_{\alpha }$$\end{document}, 0≤α<Q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0\le \alpha <Q$$\end{document} on Carnot group G\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathbb {G}}}$$\end{document} on generalized weighted Morrey spaces Mp,φ(G,w)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$M_{p,\varphi }({{\mathbb {G}}},w)$$\end{document}, where Q is the homogeneous dimension of G\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathbb {G}}}$$\end{document}. Also we give a characterization for the Spanne type boundedness of the fractional maximal commutator operator Mb,α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$M_{b,\alpha }$$\end{document} on generalized weighted Morrey spaces.
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