Two‐weight inequalities for singular integral operators satisfying a variant of Hörmander′s condition

Abstract

In this paper, we present some sufficient conditions for the boundedness of convolution operators that their kernel satisfies a certain version of Hörmander's condition, in the weighted Lebesgue spacesLp,ω(ℝn).

Commutators of sublinear operators generated by Calderón-Zygmund operator on generalized weighted Morrey spaces

“…In [12], [13], [14], [16], [20], [28] and [31], sufficient conditions on ϕ 1 and ϕ 2 for the boundedness of the maximal operator M and a Calderón-Zygmund operator K from the generalized Morrey spaces M p,ϕ1 to M p,ϕ2 for 1 < p < ∞ and from M 1,ϕ1 to W M 1,ϕ2 were obtained (see also [34], [2], [1]). In [9], the following condition was imposed on ϕ(x, r):…”

Commutators of Singular Integral Operators Satisfying a Variant of a Lipschitz Condition

“…Under the assumption of Theorem 3, several authors have studied two-weight inequalities for the convolution operator T , for example [11–13]. Recently, the authors [14] introduce a variant of the classical L r -Hörmander's condition in the scope of (2) and establish the weighted norm inequalities for singular integral operator with its kernel satisfying such a variant of the classical L r -Hörmander's condition.…”

Two-Weight Norm Inequalities for Certain Singular Integrals

“…Note that for p = q Theorem 4 and Theorem 5 were proved in [1]. In the case p = q for some sublinear operator, Theorem 4 and Theorem 5 were proved in [7]. Also, at ϕ = 1 for other type singular integral the Theorem 4 and Theorem 5 was proved in [10].…”

“…Note that for other type singular integral at ϕ = 1, Theorem 6 and Theorem 7 were proved in [10]. For some sublinear operator at p = q = 1, Theorem 6 and Theorem 7 were proved in [7].…”