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

Characterizations for the fractional maximal operator and its commutators in generalized weighted... 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Analysis and Mathematical Physics Springer Journals

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

, Volume 10 (2) – Mar 5, 2020
20 pages

Loading next page...

/lp/springer-journals/characterizations-for-the-fractional-maximal-operator-and-its-4yc7BE0Q3F
Publisher
Springer Journals
Copyright
Copyright © Springer Nature Switzerland AG 2020
ISSN
1664-2368
eISSN
1664-235X
DOI
10.1007/s13324-020-00360-9
Publisher site
See Article on Publisher Site

### Abstract

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.

### Journal

Analysis and Mathematical PhysicsSpringer Journals

Published: Mar 5, 2020