Calderón–Zygmund operators and their commutators on generalized weighted Orlicz–Morrey spaces

Abstract

In this paper, we obtain the necessary and sufficient conditions for the weak/strong boundedness of the Calderón–Zygmund operators in generalized weighted Orlicz–Morrey spaces. We also study the boundedness of the commutators of Calderón–Zygmund operators on these spaces. Moreover, the boundedness of Calderón–Zygmund operators in the vector-valued setting is given.

Boundedness criteria for the fractional integral and fractional maximal operator on Morrey spaces generated by the Gegenbauer differential operator

“…We will see later the relation () taken into account in the definition of the $$$ G $$$‐fractional integral and the $$$ G $$$‐fractional maximal function. This approach, used in [19, 20], where: F. Chiarenza, M. Frasca, and P. Longo, $$$ {W}^{2,p} $$$‐ solvability of the Dirichlet problem for nondivergence elliptic‐equations with VMO coefficients, Trans.…”

“…We will see later the relation (2.2) taken into account in the definition of the G-fractional integral and the G-fractional maximal function. This approach, used in [19,20], where: [19] F. Chiarenza, M. Frasca, and P. Longo, W…”