Boundedness of Certain Calderón-Zygmund Type Singular Integrals on Morrey Spaces

doi:10.1007/s40840-024-01802-4

	Boundedness of Certain Calderón-Zygmund Type Singular Integrals on Morrey Spaces
	Xin, Yinping1,2 ; Yang, Sibei 1
	2025-01
发表期刊	BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY
卷号	48 期号:1
摘要	Let beta is an element of(0,n)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta \in (0,n)$$\end{document}. In this paper, we study the boundedness of the singular integral T(f)(x):=p.v.integral Rn Omega(y)\|y\|n-beta f(x-y)dy,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} T(f)(x):=\mathrm {p.v.}\int _{\mathbb {R}<^>n}\frac{\Omega (y)}{\|y\|<^>{n-\beta }}f(x-y)\,dy, \end{aligned}$$\end{document}which can be viewed as an extension of the classical Calder & oacute;n-Zygmund singular integral, on Morrey spaces. Precisely, let q is an element of(1,infinity)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q\in (1,\infty )$$\end{document} and theta is an element of(0,n]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\theta \in (0,n]$$\end{document}. We prove that, for any f is an element of Mq theta(Rn)boolean AND M1 theta(Rn)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f\in \mathcal {M}<^>{\theta }_q(\mathbb {R}<^>n)\cap \mathcal {M}<^>{\theta }_1(\mathbb {R}<^>n)$$\end{document}, Tf is an element of Mq theta(Rn)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Tf\in \mathcal {M}<^>{\theta }_q(\mathbb {R}<^>n)$$\end{document} and & Vert;Tf & Vert;Mq theta(Rn)<= C & Vert;f & Vert;Mq theta(Rn)+beta(q-1)nqn(q-1)-beta qq & Vert;f & Vert;M1 theta(Rn),\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \Vert Tf\Vert _{\mathcal {M}<^>{\theta }_q(\mathbb {R}<^>n)}\le C\left[ \Vert f\Vert _{\mathcal {M}<^>{\theta }_q(\mathbb {R}<^>n)} +\frac{\beta <^>{\frac{(q-1)n}{q}}}{\root q \of {n(q-1)-\beta q}}\Vert f\Vert _{\mathcal {M}<^>{\theta }_1(\mathbb {R}<^>n)}\right] , \end{aligned}$$\end{document}where the constant C is independent of beta\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta $$\end{document} and f, and Mq theta(Rn)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {M}<^>{\theta }_q(\mathbb {R}<^>n)$$\end{document} denotes the Morrey space on Rn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {R}<^>n$$\end{document}.
关键词	Calder & oacute n-Zygmund type singular integral Weight Morrey space
DOI	10.1007/s40840-024-01802-4
收录类别	SCIE
ISSN	0126-6705
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:001370652000002
出版者	SPRINGERNATURE
原始文献类型	Article
EISSN	2180-4206
引用统计	被引频次[WOS]：0 [WOS记录] [WOS相关记录]
文献类型	期刊论文
条目标识符	http://ir.lzufe.edu.cn/handle/39EH0E1M/38515
专题	信息工程与人工智能学院
通讯作者	Yang, Sibei
作者单位	1.Lanzhou Univ, Sch Math & Stat, Gansu Key Lab Appl Math & Complex Syst, Lanzhou 730000, Peoples R China; 2.Lanzhou Univ Finance & Econ, Sch Informat Engn & Artificial Intelligence, Lanzhou 730010, Peoples R China
第一作者单位	信息工程与人工智能学院
推荐引用方式 GB/T 7714	Xin, Yinping,Yang, Sibei. Boundedness of Certain Calderón-Zygmund Type Singular Integrals on Morrey Spaces[J]. BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY,2025,48(1).
APA	Xin, Yinping,&Yang, Sibei.(2025).Boundedness of Certain Calderón-Zygmund Type Singular Integrals on Morrey Spaces.BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY,48(1).
MLA	Xin, Yinping,et al."Boundedness of Certain Calderón-Zygmund Type Singular Integrals on Morrey Spaces".BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY 48.1(2025).