arXiv subjects
Publications and source records attributed to Ferit Gurbuz.
In this paper we give BMO (bounded mean oscillation) space estimates for commutators of fractional type sublinear operators in generalized Morrey spaces on Heisenberg groups. The boundedness conditions are also formulated in terms of Zygmund type integral inequalities.
The aim of this paper is to get the boundedness of certain multi-sublinear operators generated by multilinear fractional integral operators on the product generalized local Morrey spaces under generic size conditions which are satisfied by most of the operators in harmonic analysis. We also prove that the commutators of multilinear operators generated by local campanato functions and multilinear fractional integral operators are also bounded on the product generalized local Morrey spaces.
In this paper, we consider the norm inequalities for sublinear operators with rough kernel generated by fractional integrals and commutators on generalized local Morrey spaces and on generalized vanishing local Morrey spaces including their weak versions under generic size conditions which are satisfied by most of the operators in harmonic analysis, respectively. As an example to the conditions of these theorems are satisfied, we can consider the Marcinkiewicz operator.
The aim of this paper is to get the boundedness of certain sublinear operators with rough kernel generated by Calderón-Zygmund operators on the generalized weighted Morrey spaces under generic size conditions which are satisfied by most of the operators in harmonic analysis. We also prove that the commutator operators formed by BMO functions and certain sublinear operators with rough kernel are also bounded on the generalized weighted Morrey spaces. Marcinkiewicz operator which satisfies the conditions of these theorems can be considered as an example.
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, 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 establihes 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, respec- tively. At last, parabolic Marcinkiewicz operator which satisfies the conditions of these theorems can be considered as an example.