The aim of this paper is to establish the necessary and sufficient conditions for the compactness of fractional integral commutator[b,I_(γ)]which is generated by fractional integral I_(γ)and function b∈Lip_(β)(μ)...The aim of this paper is to establish the necessary and sufficient conditions for the compactness of fractional integral commutator[b,I_(γ)]which is generated by fractional integral I_(γ)and function b∈Lip_(β)(μ)on Morrey space over non-homogeneous metric measure space,which satisfies the geometrically doubling and upper doubling conditions in the sense of Hytonen.Under assumption that the dominating functionλsatisfies weak reverse doubling condition,the author proves that the commutator[b,I_(γ)]is compact from Morrey space M_(q)^(p)(μ)into Morrey space M_(t)^(s)(μ)if and only if b∈Lip_(β)(μ).展开更多
In this article,the viscoelastic damped was equation in three-dimensional cylindrical domain were studied by using a second-order differential inequality.We proved a Phragm´en-Lindelof alternative results,i.e.,th...In this article,the viscoelastic damped was equation in three-dimensional cylindrical domain were studied by using a second-order differential inequality.We proved a Phragm´en-Lindelof alternative results,i.e.,the smooth solutions either grow or decay exponentially as the distance from the entry section tends to infinity.Our results can be seen as a version of the Saint-Venant principle.展开更多
基金Supported by the Scientific Startup Foundation for Doctors of Northwest Normal University(Grant No.0002020203)the Innovation Fund Project for Higher Education of Gansu Province(Grant No.2020A-010)。
文摘The aim of this paper is to establish the necessary and sufficient conditions for the compactness of fractional integral commutator[b,I_(γ)]which is generated by fractional integral I_(γ)and function b∈Lip_(β)(μ)on Morrey space over non-homogeneous metric measure space,which satisfies the geometrically doubling and upper doubling conditions in the sense of Hytonen.Under assumption that the dominating functionλsatisfies weak reverse doubling condition,the author proves that the commutator[b,I_(γ)]is compact from Morrey space M_(q)^(p)(μ)into Morrey space M_(t)^(s)(μ)if and only if b∈Lip_(β)(μ).
基金Supported by the Guangdong Natural Science foundation(2023A1515012044)Special Project of Guangdong Province in Key Fields of Ordinary Colleges and Universities(2023ZDZX4069)+1 种基金the Research Team of Guangzhou Huashang College(2021HSKT01)Guangzhou Huashang College’s Characteristic Research Projects(2024HSTS09)。
文摘In this article,the viscoelastic damped was equation in three-dimensional cylindrical domain were studied by using a second-order differential inequality.We proved a Phragm´en-Lindelof alternative results,i.e.,the smooth solutions either grow or decay exponentially as the distance from the entry section tends to infinity.Our results can be seen as a version of the Saint-Venant principle.
