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 thes...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.展开更多
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)。
文摘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.
