Matrix-weighted Besov-type and Triebel-Lizorkin-type spaces I: Ap-dimensions of matrix weights and'-transform characterizations

被引:0
作者
Bu, Fan [1 ]
Hytonen, Tuomas [2 ]
Yang, Dachun [1 ]
Yuan, Wen [1 ]
机构
[1] Beijing Normal Univ, Sch Math Sci, Lab Math & Complex Syst, Minist Educ China, Beijing 100875, Peoples R China
[2] Aalto Univ, Dept Math & Syst Anal, POB 11100, Aalto 00076, Finland
关键词
MORREY SPACES; PSEUDODIFFERENTIAL-OPERATORS; MOLECULAR DECOMPOSITION; SINGULAR-INTEGRALS; A(P) WEIGHTS; DISTRIBUTIONS; EMBEDDINGS; INEQUALITIES; MULTIPLIERS; EQUATIONS;
D O I
10.1007/s00208-024-03059-5
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Let , and It is well known that Besov-type spaces. B s,t p,q with and Triebel-Lizorkin-type spaces. F s,t p,q with when or with when t = 0 on Rn consist of a general family of function spaces that cover not only the well-known Besov and Triebel-Lizorkin spaces and (when t = 0) but also several other function spaces of interest, such as Morrey spaces and Q spaces. In three successive articles, the authors develop a complete real-variable theory of matrix-weighted Besov-type spaces (W) and matrix-weighted Triebel-Lizorkin-type spaces (W) on Rn, where W is a matrixvalued Muckenhoupt Ap weight. This article is the first one, whosemain novelty exists in that the authors introduce the new concept, Ap-dimensions of matrix weights, and intensively study their properties, especially those elaborate properties expressed via reducing operators. The authors then introduce the spaces (W) and (W) and, using Ap-dimensions and their nice properties, the authors establish the.-transform characterization of (W) and (W). The Ap-dimensions of matrix weights
引用
收藏
页码:6105 / 6185
页数:81
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