Herz Type Spaces With Variable Exponents And Their Applications

The dissertation is devoted to the Herz type spaces with variable exponents and their applications. The results cover classical Herz type spaces with constant exponents. It is arranged as follows.In Chapter1, there are the background of the research, the definition of Herz space with variable exponents and main results of the dissertation.In Chapter2, the boundedness of vector-valued Hardy-Littlewood maximal operator on non-homogen-eous Herz spaces with variable exponents Ka(·)p(·),q(Rn) and homogeneous Herz spaces with variable expo-nents Ka(·)p(·),q(Rn) are obtained.In Chapter3, the Herz type Besov and Triebel-Lizorkin spaces with variable exponents are in-troduced. Then equivalent quasi-norms of Herz type Besov and Triebel-Lizorkin spaces with variable exponents by Peetre’s maximal operator are given.In Chapter4, the Herz type Hardy spaces with variable exponents HKa(·)p(·),q(Rn) and HK(·)p(·),q(Rn) are introduced. Then their atomic and molecular decompositions are given. Finally, some singular integrals axe proved to be bounded on these spaces by their atomic and molecular decompositions.