变指数Herz-Morrey空间上一些算子及其交换子的有界性研究.pdfVIP

Research on Boundedness of some Operators and their Commutators on Herz-Morrey spaces with variable exponents Abstract In this thesis, we m ainly study the boundedness of some operators and their commutators on Herz-Morrey spaces w ith variable exponents. First of all we in tro ­ duce the background knowledge and definitions of the Lebesgue spaces w ith variable exponent L p(^)(Rn) , the Herz-Morrey spaces w ith variable exponents M K p^A( )(R™ ), MKKaP()^)A(Rn) and Hardy type operators which we studied. A t the same tim e we also give some lemmas which is necessary in the process of the proof of theorems . Then we m ainly study the boundedness of variable exponent fractional Hardy operators on Herz-Morrey spaces w ith variable exponent by the nature of the Hardy type operators as well as the estimations of the sphere norms.Furthermore we extend the results to the m ultilinear cases. A t the last, we m ainly ta lk about the boundedness of the sub-linear operators and their commutators on Herz-Morrey spaces w ith vari­ able exponents M F C ^•^(R ™ ) by the definitions of the sub-linear and some im portant lemmas . Keywords: the fractional Hardy operators w ith variable exponent; M u ltilin ­ ear n-dimensional fractional Hardy operators w ith variable exponent; the sub-linear operators; commutators; Herz-Morrey spaces w ith variable exponent; the Herz-Morrey spaces w ith variable exponents; BM O space; Lipschitz space Subject Classifcation(AMS 201 0): 42B20, 42B25 万方数据