Pointwise Characterizations of Besov and Triebel–Lizorkin Spaces with Generalized Smoothness and Their Applications  

作　　者：Zi Wei LI Da Chun YANG Wen YUAN 

机构地区：[1]Laboratory of Mathematics and Complex Systems(Ministry of Education of China),School of Mathematical Sciences,Beijing Normal University,Beijing 100875,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2022年第4期623-661,共39页数学学报（英文版）

基　　金：the National Natural Science Foundation of China(Grant Nos.11971058,12071197 and 11871100);the National Key Research and Development Program of China(Grant No.2020YFA0712900)。

摘　　要：In this article,the authors first establish the point wise characterizations of Besov and Triebel-Lizorkin spaces with generalized smoothness on R;via the Hajlasz gradient sequences,which serve as a way to extend these spaces to more general metric measure spaces.Moreover,on metric spaces with doubling measures,the authors further prove that the Besov and the Triebel-Lizorkin spaces with generalized smoothness defined via Hajlasz gradient sequences coincide with those defined via hyperbolic fillings.As an application,some trace theorems of these spaces on Ahlfors regular spaces are established.

关 键 词：Besov space Triebel-Lizorkin space generalized smoothness Hajlasz gradient hyperbolic filling trace 

分 类 号：O177.91[理学—数学]