The boundedness of certain sublinear operators with rough kernel generated by Calder\'on-Zygmund operators and their commutators on generalized weighted Morrey spaces

The aim of this paper is to get the boundedness of certain sublinear operators with rough kernel generated by Calder\'on-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.Comment: arXiv admin note: substantial text overlap with arXiv:1602.07853, arXiv:1603.06739, arXiv:1603.04088, arXiv:1603.03469, arXiv:1602.08096; text overlap with arXiv:1212.6928 by other author

Vanishing generalized Morrey spaces and commutators of Marcinkiewicz integrals with rough kernel associated with Schr\"odinger operator

Let L=-{\Delta}+V(x) be a Schrodinger operator, where {\Delta} is the Laplacian on while nonnegative potential V(x) belonging to the reverse Holder class. We establish the boundedness of the commutators of Marcinkiewicz integrals with rough kernel associated with Schrodinger operator on vanishing generalized Morrey spaces.Comment: arXiv admin note: text overlap with arXiv:1602.0785

Weighted anisotropic Morrey Spaces estimates for anisotropic maximal operators

The aim of this paper can give weighted anisotropic Morrey Spaces estimates for anisotropic maximal functions

Parabolic sublinear operators with rough kernel generated by parabolic Calder\'on-Zygmund operators and parabolic local Campanato space estimates for their commutators on the parabolic generalized local Morrey spaces

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.Comment: arXiv admin note: substantial text overlap with arXiv:1602.07853, arXiv:1602.07468; substantial text overlap with arXiv:1212.6928 by other author

Some estimates for generalized commutators of rough fractional maximal and integral operators on generalized weighted Morrey spaces

In this paper, we establish BMO estimates for generalized commutators of rough fractional maximal and integral operators on generalized weighted Morrey spaces, respectively.Comment: 16 pages. arXiv admin note: text overlap with arXiv:1603.0346

Multi-sublinear operators generated by multilinear fractional integral operators and commutators on the product generalized local Morrey spaces

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.Comment: arXiv admin note: substantial text overlap with arXiv:1603.04088; text overlap with arXiv:1212.6928 by other author

Adams-Spanne type estimates for the commutators of fractional type sublinear operators in generalized Morrey spaces on Heisenberg groups

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

Sublinear operators with rough kernel generated by fractional integrals and commutators on generalized vanishing 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.Comment: arXiv admin note: text overlap with arXiv:1603.04088, arXiv:1604.01538, arXiv:1603.03469, arXiv:1602.07468, arXiv:1602.08096, arXiv:1602.08788; text overlap with arXiv:1212.6928, arXiv:1208.4788 by other author

Adams-Spanne type estimates for parabolic sublinear operators and their commutators by with rough kernels on parabolic generalized Morrey spaces

The aim of this paper is to give Adams-Spanne type estimates for parabolic sublinear operators and their commutators by with rough kernels generated by parabolic fractional integral operators under generic size conditions which are satisfied by most of the operators in harmonic analysis. Their endpoint estimates are also disposed

A class of sublinear operators and their commutators by with rough kernels on vanishing generalized Morrey spaces

In this paper, we consider the boundedness of a class of sublinear operators and their commutators by with rough kernels associated with Calderon-Zygmund operator, Hard-Littlewood maximal operator, fractional integral operator, fractional maximal operator by with rough kernels both on vanishing generalized Morrey spaces and vanishing Morrey spaces, respectively.Comment: arXiv admin note: text overlap with arXiv:1602.07853, arXiv:1603.0346