Multilinear Singular Integrals with Rough Kernel Multilinear Singular Integrals with Rough Kernel期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

按检索

Multilinear Singular Integrals with Rough Kernel

作者姓名：

作者单位：

[1]DepartmentofMathermatics,BeijngNormalUniversity,Beijing100875 [2]DepartmentofMathermatics,ZhejiangUniversity（atXixiCampus）,Hangzhou310028

摘要：

关键词：

多重线性算子奇异积分利普希茨空间 Triebel－Lizorkin空间粗糙核 Lipschitz空间

Multilinear Singular Integrals with Rough Kernel

ShanZhenLU HuoXiongWU PuZHANG.Multilinear Singular Integrals with Rough Kernel[J].Acta Mathematica Sinica,2003,19(1):51-62.

Authors:

Email author" target="_blank">Shan?Zhen?Lu Email author Huo?Xiong?Wu Pu?Zhang

Institution:

(1) Department of Mathematics, Beijing Normal University, Beijing 100875, P. R. China;(2) Department of Mathematics, Zhejiang University (at Xixi Campus), Hangzhou 310028, P. R. China

Abstract:

For a class of multilinear singular integral operators T _A,

$T_{A} f{\left( x \right)} = {\int_{\mathbb{R}^{n} } {\frac{{\Omega {\left( {x - y} \right)}}} {{{\left| {x - y} \right|}^{{n + m - 1}} }}} }R_{m} {\left( {A;x,y} \right)}f{\left( y \right)}dy$

where R _m(A; x, y) denotes the m-th Taylor series remainder of A at x expanded about y, A has derivatives of order m − 1 in $\ifmmode\expandafter\dot\else\expandafter\.\fi{\Lambda }_{\beta } {\left( {0 < \beta < 1} \right)},\Omega {\left( x \right)} \in L^{s} {\left( {S^{{n - 1}} } \right)}{\left( {s \geqslant \frac{n} {{n - \beta }}} \right)},$ is homogeneous of degree zero, the authors prove that T _A is bounded from L ^p(ℝⁿ) to $L^{q} {\left( {\mathbb{R}^{n} } \right)}{\left( {\frac{1} {p} - \frac{1} {q} = \frac{\beta } {n},1 < p < \frac{n} {\beta }} \right)}$ and from L ¹(ℝⁿ) to L ^{n/(n−β),∞}(ℝⁿ) with the bound $C{\sum\nolimits_{{\left| \gamma \right|} = m - 1} {{\left\| {D^{\gamma } A} \right\|}} }_{{\ifmmode\expandafter\dot\else\expandafter\.\fi{\Lambda }_{\beta } }} .$ And if Ω has vanishing moments of order m − 1 and satisfies some kinds of Dini regularity otherwise, then T _A is also bounded from L ^p(ℝⁿ) to $\ifmmode\expandafter\dot\else\expandafter\.\fi{F}^{{\beta ,\infty }}_{p} {\left( {\mathbb{R}^{n} } \right)}{\left( {1 < {s}\ifmmode{'}\else$'$\fi < p < \infty } \right)}$ with the bound $C{\sum\nolimits_{{\left| \gamma \right|} = m - 1} {{\left\| {D^{\gamma } A} \right\|}} }_{{\ifmmode\expandafter\dot\else\expandafter\.\fi{\Lambda }_{\beta } }} .$ Supported by the National 973 Project (G1990751) and SEDF of China (20010027002)

Keywords:

Multilinear operator Singular integral Lipschitz spaces Triebel-Lizorkin spaces Rough kernel

本文献已被维普 SpringerLink 等数据库收录！

设为首页 | 免责声明 | 关于勤云 | 加入收藏