Multilinear analysis on metric spaces

被引：47

作者：

Grafakos, Loukas ^{[2
]}

Liu, Liguang ^{[3
]}

Maldonado, Diego ^{[4
]}

Yang, Dachun ^{[1
]}

机构：

[1] Beijing Normal Univ, Sch Math Sci, Lab Math & Complex Syst, Minist Educ, Beijing 100875, Peoples R China

[2] Univ Missouri, Dept Math, Columbia, MO 65211 USA

[3] Renmin Univ China, Sch Informat, Dept Math, Beijing 100872, Peoples R China

[4] Kansas State Univ, Dept Math, Manhattan, KS 66506 USA

来源：

DISSERTATIONES MATHEMATICAE | 2014年 / 497期

关键词：

space of homogeneous type; multilinear Calderon Zygmund operator; multilinear weighted estimate; paraproduct; bilinear T1-theorem; quadratic T1 type theorem; bilinear multiplier; Besov space; Triebel-Lizorkin space; WEIGHTED NORM INEQUALITIES; EUCLIDEAN N-SPACE; SINGULAR INTEGRAL-OPERATORS; TRIEBEL-LIZORKIN SPACES; HARDY-SPACES; MAXIMAL FUNCTIONS; LIPSCHITZ-SPACES; BILINEAR OPERATORS; NONSMOOTH KERNELS; HOMOGENEOUS TYPE;

D O I：

10.4064/dm497-0-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The multilinear Calderon-Zygmund theory is developed in the setting of RD-spaces which are spaces of homogeneous type equipped with measures satisfying a reverse doubling condition. The multiple-weight multilinear Calderon-Zygmund theory in this context is also developed in this work. The bilinear T1-theorems for Besov and Triebel-Lizorkin spaces" in the full range of exponents are among the main results obtained. Multi linear vector-valued T1 type theorems on Lebesgue spaces, Besov spaces, and Triebel-Lizorkin spaces are also proved. Applications include the boundedness of paraproducts and bilinear multiplier operators on products of Besov and Triebel-Lizorkin spaces.

引用

页码：1 / 121

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