Boundedness Of Integral Operators And Their Commutators On Morrey Type Spaces

The boundedness of integral operators in different weighted function spaces is always one of the hot topics in harmonic analysis,and its contents and ideas are widely used in PDE,complex analysis,wavelet analysis and many other mathematical fields.In this paper,we study the boundedness of singular integral operators with rough kernel and their commutators on new weighted generalized Morrey spaces and the boundedness of multilinear Calderón-Zygmund operators on weighted Morrey spaces.The main work is as follows:In order to investigate the boundedness of singular integral operators and their commutators with rough kernels on new weighted generalized Morrey spaces.Some common estimation methods,such asA_p weight function class theorems and H（?）lder inequalities,are used in this paper,the boundedness of singular integral operators and their commutators with rough kernel on new weighted generalized Morrey spaces is proved.Secondly,we study the boundedness of multilinear Calderón-Zygmund operators on weighted Morrey spaces.In this paper,we obtain the double weighted inequalities of multilinear Calderón-Zygmund operators on weighted Morrey spaces by using the properties of the classes of multilinear vector weight functions,multilinear H（?）lder inequalities,multilinear inverse H（?）lder inequalities and the related properties of the classes of weight functionsA_p andA_p,q.