Rough singular integrals associated with surfaces of Van der Corput type

被引：0
作者：
Liu Feng [1 ]
Wu Huo-xiong [1 ]
机构：
[1] Xiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China
来源：
APPLIED MATHEMATICS-A JOURNAL OF CHINESE UNIVERSITIES SERIES B | 2014年 / 29卷 / 01期
基金：
中国国家自然科学基金;
关键词：
Singular integrals; surfaces of Van der Corput type; maximal operators; Littlewood-Paley theory; Fourier transform estimates; L-P BOUNDS; MAXIMAL FUNCTIONS; OPERATORS; KERNELS;
D O I：
10.1007/s11766-014-3149-7
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, the authors establish the L (p) -mapping properties for a class of singular integrals along surfaces in a"e (n) of the form {I center dot(|u|)u': u a a"e (n) } as well as the related maximal operators provided that the function I center dot satisfies certain oscillatory integral estimates of Van der Corput type, and the integral kernels are given by the radial function {ie86-1} for gamma > 1 and the sphere function {ie86-2} for some beta > 0, which is distinct from H (1)(S (n-1)).
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页码：86 / 100
页数：15
相关论文
共 27 条
  • [1] Al-Qassem H., 2001, TURKISH J MATH, V25, P519
  • [2] Al-Qassem H. M., 2006, J INEQUAL APPL, V2006, P1
  • [3] Singular integrals with rough kernels
    Al-Salman, A
    Pan, YB
    [J]. CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 2004, 47 (01): : 3 - 11
  • [4] Singular integrals with rough kernels in L log L(Sn-1)
    Al-Salman, A
    Pan, YB
    [J]. JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2002, 66 : 153 - 174
  • [5] Al-Salman A, 2008, ANAL MATH, V34, P163, DOI 10.1007/s10476-008-0301-8
  • [6] [Anonymous], 1993, Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals
  • [7] ON SINGULAR INTEGRALS
    CALDERON, AP
    ZYGMUND, A
    [J]. AMERICAN JOURNAL OF MATHEMATICS, 1956, 78 (02) : 289 - 309
  • [8] Chen JC, 2001, MATH NACHR, V227, P33, DOI 10.1002/1522-2616(200107)227:1<33::AID-MANA33>3.0.CO
  • [9] 2-0
  • [10] On singular integrals along surfaces related to black spaces
    Chen, LK
    Fan, D
    [J]. INTEGRAL EQUATIONS AND OPERATOR THEORY, 1997, 29 (03) : 261 - 268
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