Variable Exponent Besov And Triebel-Lizorkin Spaces

The dissertation is devoted to the Besov and Triebel-Lizorkin spaces with variable exponents and their applications. The results cover classical Besov and Triebel-Lizorkin spaces with constant exponents and some new type Triebel-Lizorkin space. It is arranged as follows.In Chapter 1, there are the background of the research and some symbols.In Chapter 2, the Herz type Besov and Triebel-Lizorkin spaces with three variable exponents are introduced. Then equivalent quasi-norms of Herz type Besov and Triebel-Lizorkin spaces with variable exponents by Peetre's maximal operator are given.In Chapter 3, variable integral exponent Besov and Triebel-Lizorkin spaces associated with a nonnegative self-adjoint operator are introduced. Then we prove their atomic and molecular decompositions.In Chapter 4, the B_W~u type Morrey-Triebel-Lizorkin spaces with variable smoothness and integrability are introduced. Then their atomic and molecular decompositions are given.