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

• 作者: Zi Wei LI Da Chun YANG Wen YUAN
• 来源期刊: 数学学报（英文版）
• 年，卷（期）: 2022,（4）
• 页码范围: 623-661
• 页数: 39页
• 语种: 英文

摘要

In this article,the authors first establish the pointwise characterizations of Besov and Triebel-Lizorkin spaces with generalized smoothness on Rn via the Haj?asz 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 Haj?asz gradient sequences coincide with those defined via hyperbolic fillings.As an application,some trace theorems of these spaces on Ahlfors regular spaces are established.