p-adic singular integrals and their commutators in 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...

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

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.

Adams-spanne Type Estimates for Certain Sublinear Operators and Their Commutators Generated by Fractional Integrals in Generalized Morrey Spaces on Heisenberg Groups and Some Applications

In this paper we consider the Spanne type boundedness of sublinear operators and prove the Adams type boundedness theorems for these operators and also give BMO (bounded mean oscillation space) estimates for their commutators in generalized Morrey spaces on Heisenberg groups. The boundedness conditions are formulated in terms of Zygmund type integral inequalities. Based on the properties of the...

Notes on Commutators of Fractional Integral Operatros on Generalized Morrey Spaces

We show that b ∈ BMO( n) if and only if the commutator [b, Iα] of the multiplication operator by b and the fractional integral operator Iα is bounded from generalized Morrey spaces Lp,φ( n) to Lq,φ q/p ( n), where φ is non-decreasing, and 1 < p < ∞, 0 < α < n and 1/q = 1/p− α/n.