Rough singular integrals and maximal operators with mixed homogeneity along compound curves

被引：12

作者：

Liu, Feng ^{[1
]}

Wu, Huoxiong ^{[1
]}

机构：

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

来源：

MATHEMATISCHE NACHRICHTEN | 2014年 / 287卷 / 10期

关键词：

Singular integrals; maximal operators; mixed homogeneity; rough kernels; Fourier transform estimates; L-P BOUNDS; SURFACES; KERNELS;

D O I：

10.1002/mana.201300016

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The parabolic singular integrals along certain compound curves as well as the related maximal operators are considered. Under rather weakened size conditions on the integral kernels both on the unit sphere and in the radial direction, the L-p-mapping properties for such operators are established. Some previous results are greatly extended and improved. (C) 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

引用

页码：1166 / 1182

页数：17

共 28 条

[1]

Al-Qassem H. M., 2006, J INEQUAL APPL, V2006, P1

[2]

Al-Qassem HM., 2005, KODAI MATH J, V28, P494, DOI [10.2996/kmj/1134397763, DOI 10.2996/KMJ/1134397763]

[3] Maximal operators with rough kernels on product domains [J].

Al-Salman, A .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2005, 311 (01) :338-351

[4]

AL-SALMAN A., 2010, Proc. A. Razmadze Math. Inst., V154, P21

[5]

Al-Salman A, 2008, ANAL MATH, V34, P163, DOI 10.1007/s10476-008-0301-8

[6] Parabolic Marcinkiewicz Integrals along Surfaces on Product Domains [J].

Al-Salman, Ahmad .

ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2011, 27 (01) :1-18

[7]

[Anonymous], 2012, J INEQUAL APPL, DOI DOI 10.5402/2012/970685

[8] ON SINGULAR INTEGRALS [J].

CALDERON, AP ;

ZYGMUND, A .

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

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

CHEN, LK ;

LIN, H .

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

[10] Lp Bounds for the parabolic singular integral operator [J].

Chen, Yanping ;

Wang, Feixing ;

Yu, Wei .

JOURNAL OF INEQUALITIES AND APPLICATIONS, 2012, :1-9

← 1 2 3 →