In this paper, we will study the boundedness of a large class of sublinear operators with rough kernel T on the generalized local Morrey spaces LM

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Abstract:In this paper, the author introduces parabolic generalized local Morrey spaces and gets the boundedness of a large class of parabolic rough operators on them. The author also establishes the parabolic local Campanato space estimates for their commutators on parabolic generalized local Morrey spaces. As its special cases, the corresponding results of parabolic sublinear operators with rough kernel and their commutators can be deduced, respectively. At last, parabolic Marcinkiewicz operator which satisfies the conditions of these theorems can be considered as an example.

Abstract. In this paper, we establish BMO estimates for generalized commutators of rough fractional maximal and integral operators on generalized weighted Morrey spaces, respectively.

In this paper, we study the boundedness results for a large class of pseudo-differential operators with smooth symbols on weighted Morrey and Weighted fractional Sobolev-Morrey spaces, respectively.