| The function spaces with variable exponents and the boundedness of related operators are important issues in harmonic analysis,which has attracted extensive attention on scholars at home and abroad in recent years.The dissertation is devoted to the boundedness of several Hardy-type operators with rough kernels on the central Morrey spaces with variable exponents.It is arranged as follows.In chapter 1,we briefly introduce the background and the recent development related to this topic at home and abroad.Then we recall the Lebesgue space with variable exponents and review the important lemmas of it.In addition,we introduce the definition of central Morrey spaces with variable exponents.Finally,we summarize the main contents of this thesis.In chapter 2,we study the boundedness of Hardy operator,adjoint operator and their commutator with rough kernels on the central Morrey spaces with variable exponents.In chapter 3,we study the boundedness of the fractional Hardy operator,adjoint operator and their commutator with rough kernels on the central Morrey spaces with variable exponents.In chapter 4,we study the boundedness of the bilinear fractional Hardy operator,adjoint operator and their commutator with rough kernels on the central Morrey spaces with variable exponents.Then,we derive the relevant corollary of the boundedness of the multilinear cases on the central Morrey spaces with variable exponents.In chapter 5,the main results of the full paper are summarized and we present the relevant questions and research direction in the future. |
