We establish a pointwise property for homogeneous fractional Sobolev spaces in domains with non-empty boundary,extending a similar result of Koskela–Yang–Zhou.We use this to show that a conformal map from the unit d...We establish a pointwise property for homogeneous fractional Sobolev spaces in domains with non-empty boundary,extending a similar result of Koskela–Yang–Zhou.We use this to show that a conformal map from the unit disk onto a simply connected planar domain induces a bounded composition operator from the borderline homogeneous fractional Sobolev space of the domain into the corresponding space of the unit disk.展开更多
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Supported by the Academy of Finland via Centre of Excellence in Analysis and Dynamics Research(Grant No.323960)ISF(Grant No.1149/18)。
文摘We establish a pointwise property for homogeneous fractional Sobolev spaces in domains with non-empty boundary,extending a similar result of Koskela–Yang–Zhou.We use this to show that a conformal map from the unit disk onto a simply connected planar domain induces a bounded composition operator from the borderline homogeneous fractional Sobolev space of the domain into the corresponding space of the unit disk.
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.
