On rough singular integrals along real-analytic submanifolds

被引：2

作者：

Liu, Feng ^{[3
]}

Wu, Huoxiong ^{[4
]}

Xue, Qingying ^{[1
,2
]}

机构：

[1] Beijing Normal Univ, Sch Math Sci, Beijing 100875, Peoples R China

[2] Minist Educ, Lab Math & Complex Syst, Beijing 100875, Peoples R China

[3] Shandong Univ Sci & Technol, Coll Math & Syst Sci, Qingdao 266590, Shandong, Peoples R China

[4] Xiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China

来源：

FORUM MATHEMATICUM | 2020年 / 32卷 / 02期

关键词：

Singular integrals; maximal functions; rough kernels; real-analytic submanifolds; MAXIMAL FUNCTIONS; KERNELS; OPERATORS; TRANSFORM; SPACES;

D O I：

10.1515/forum-2019-0126

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Under some pretty much weaker size conditions assumed on the integral kernels both on the unit sphere and in the radial directions, the L-p boundedness was given for the rough singular integrals defined by translates of a real-analytic submanifold in R-n. Certain L-p estimates for the corresponding maximal rough singular integrals were also established.

引用

页码：361 / 380

页数：20

共 30 条

[1]

Al-Qassem H. M., 2006, J INEQUAL APPL, V2006

[2]

Al-Qassem H. M., 2005, Kodai Math. J., V28, P494, DOI [10.2996/kmj/1134397763, DOI 10.2996/KMJ/1134397763]

[3] On certain estimates for Marcinkiewicz integrals and extrapolation [J].

Al-Qassem, Hussain ;

Pan, Yibiao .

COLLECTANEA MATHEMATICA, 2009, 60 (02) :123-145

[4] On a class of singular integral operators with rough kernels [J].

Al-Salman, A .

CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 2006, 49 (01) :3-10

[5]

Al-Salman A, 2005, COLLECT MATH, V56, P47

[6] Singular integrals with rough kernels in L log L(Sn-1) [J].

Al-Salman, A ;

Pan, YB .

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2002, 66 :153-174

[7]

Al-Salman A, 2008, J OPERAT THEOR, V59, P263

[8] SPACES LP, WITH MIXED NORM [J].

BENEDEK, A ;

PANZONE, R .

DUKE MATHEMATICAL JOURNAL, 1961, 28 (03) :301-&

[9] ON SINGULAR INTEGRALS [J].

CALDERON, AP ;

ZYGMUND, A .

AMERICAN JOURNAL OF MATHEMATICS, 1956, 78 (02) :289-309

[10] A MAXIMAL OPERATOR RELATED TO A CLASS OF SINGULAR-INTEGRALS [J].

CHEN, LK ;

LIN, H .

ILLINOIS JOURNAL OF MATHEMATICS, 1990, 34 (01) :120-126

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