Boundedness Of Some Operators Research

In this paper, we mainly study the boundedness of the commutators of multilinearCalderón-Zygmund integral operators and Marcinkiewicz integral operators withnon-doubling measures on generalized Morrey spaces, as well as the weak-type estimates forCalderón-Zygmund integral commutators and fractional integral commutators on weightedMorrey spaces. The whole paper is divided into five chapters.In chapter1, we introduce the background and main results about the commutators ofmultilinear Calderón-Zygmund integral operators and Marcinkiewicz integral operators withnon-doubling measures, meanwhile, we introduce the development state of the weightedMorrey spaces, it draws the main conclusions of this text.In chapter2, applying the domain decomposition method, we prove the boundedness ofcommutator of multilinear Calderón-Zygmund integral operators with non-doubling measureson generalized Morrey spaces.In chapter3, we discuss the boundedness of the commutator generated by theMarcinkiewicz integral operators and a function in RBMO on generalized Morrey spaces,when measure is non-doubling measure.In chapter4, we mainly consider the endpoint estimates for Calderón-Zygmund integralcommutators and fractional integral commutators with doubling measures on weightedMorrey spaces, by means of the estimation of the sharp maximal function, we obtain the weakboundedness of commutators.In chapter5, summing up objectively the theory of this paper, and give some opinions onabove operators theory in the future.