# Singular integral operators and a ∂¯\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\overline{\partial }}$$\end{document}-problem for (φ,ψ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\varphi ,\psi )$$\end{document}-harmonic functions

Singular integral operators and a ∂¯\documentclass[12pt]{minimal} \usepackage{amsmath}... This paper aims at proving the boundedness property of multidimensional singular integral operators associated with (φ,ψ)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$(\varphi ,\psi )$$\end{document}-harmonic functions, which are connected by the use of two orthogonal basis of the Euclidean space Rm\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${{\mathbb {R}}}^m$$\end{document}. Besides, necessary and sufficient conditions for the solvability of the ∂¯\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${\overline{\partial }}$$\end{document}-problem for such (φ,ψ)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$(\varphi ,\psi )$$\end{document}-harmonic functions are described. The basic devices that make it possible to state and prove both results are borrowed from Clifford analysis. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Analysis and Mathematical Physics Springer Journals

# Singular integral operators and a ∂¯\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\overline{\partial }}$$\end{document}-problem for (φ,ψ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\varphi ,\psi )$$\end{document}-harmonic functions

, Volume 11 (4) – Dec 1, 2021
26 pages

/lp/springer-journals/singular-integral-operators-and-a-documentclass-12pt-minimal-16t4KnIM9B
Publisher
Springer Journals
Copyright © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021
ISSN
1664-2368
eISSN
1664-235X
DOI
10.1007/s13324-021-00590-5
Publisher site
See Article on Publisher Site

### Abstract

This paper aims at proving the boundedness property of multidimensional singular integral operators associated with (φ,ψ)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$(\varphi ,\psi )$$\end{document}-harmonic functions, which are connected by the use of two orthogonal basis of the Euclidean space Rm\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${{\mathbb {R}}}^m$$\end{document}. Besides, necessary and sufficient conditions for the solvability of the ∂¯\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${\overline{\partial }}$$\end{document}-problem for such (φ,ψ)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$(\varphi ,\psi )$$\end{document}-harmonic functions are described. The basic devices that make it possible to state and prove both results are borrowed from Clifford analysis.

### Journal

Analysis and Mathematical PhysicsSpringer Journals

Published: Dec 1, 2021

Keywords: Clifford analysis; Structural sets; Singular integral operator; Higher order Lipschitz classes; ∂¯\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\overline{\partial }}$$\end{document}-problem; 30G35