Boundedness of Marcinkiewicz Integrals and Their Commutators on Generalized Weighted Morrey Spaces

Boundedness of Multilinear Integral Operators and Their Commutators on Generalized Morrey Spaces

Singular Integrals and Commutators in Generalized Morrey Spaces

The purpose of this paper is to study singular integrals whose kernels k(x; ξ) are variable, i.e. they depend on some parameter x ∈ R and in ξ ∈ R \ {0} satisfy mixed homogeneity condition of the form k(x;μξ1, . . . , μ ξn) = μ − ∑ n i=1 ik(x; ξ) with positive real numbers αi ≥ 1 and μ > 0. The continuity of these operators in L(R) is well studied by Fabes and Rivière. Our goal is to extend the...

Bmo Estimates on Vanishing Generalized Morrey Spaces for Commutators of Marcinkiewicz Integrals with Rough Kernel Associated with Schrödinger Operator

Let L = −∆ + V (x) be a Schrödinger operator, where ∆ is the Laplacian on R, while nonnegative potential V (x) belonging to the reverse Hölder class. We establish the boundedness of the commutators of Marcinkiewicz integrals with rough kernel associated with schrödinger operator on vanishing generalized Morrey spaces.

Boundedness of Littlewood-Paley operators and their commutators on Herz-Morrey spaces with variable exponent

The aim of this paper is to establish the vector-valued inequalities for Littlewood-Paley operators, including the Lusin area integrals, the Littlewood-Paley g-functions and g∗μ-functions, and their commutators on the Herz-Morrey spaces with variable exponentMK̇ p,q(·)(R n). By applying the properties of Lp(·)(Rn) spaces and the vector-valued inequalities for Littlewood-Paley operators and their...

Boundedness criteria for commutators of some sublinear operators in weighted Morrey spaces

In this paper, we obtain bounded criteria on certain weighted Morrey spaces for the commutators generalized by some sublinear integral operators and weighted Lipschitz functions. We also present bounded criteria for commutators generalized by such sublinear integral operators and weighted BMO function on the weighted Morrey spaces. As applications, our results yield the same bounded criteria fo...