Multilinear analysis on metric spaces

被引：42
|
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.
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页码：1 / 121
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