Commutators of integral operators with variable kernels on Hardy spaces
نویسنده
چکیده
Abstract. Let TΩ,α (0 ≤ α < n) be the singular and fractional integrals with variable kernel Ω(x,z), and [b,TΩ,α ] be the commutator generated by TΩ,α and a Lipschitz function b. In this paper, the authors study the boundedness of [b,TΩ,α ] on the Hardy spaces, under some assumptions such as the Lr-Dini condition. Similar results and the weak type estimates at the end-point cases are also given for the homogeneous convolution operators TΩ̃,α (0 ≤ α < n). The smoothness conditions imposed on Ω̃ are weaker than the corresponding known results.
منابع مشابه
Sharp maximal and weighted estimates for multilinear iterated commutators of multilinear integrals with generalized kernels
In this paper, the authors establish the sharp maximal estimates for the multilinear iterated commutators generated by [Formula: see text] functions and multilinear singular integral operators with generalized kernels. As applications, the boundedness of this kind of multilinear iterated commutators on the product of weighted Lebesgue spaces and the product of variable exponent Lebesgue spaces ...
متن کاملCommutators of the Hardy-Littlewood Maximal Operator with BMO Symbols on Spaces of Homogeneous Type
Weighted L for p ∈ 1,∞ and weak-type endpoint estimates with general weights are established for commutators of the Hardy-Littlewood maximal operator with BMO symbols on spaces of homogeneous type. As an application, a weighted weak-type endpoint estimate is proved for maximal operators associated with commutators of singular integral operators with BMO symbols on spaces of homogeneous type. Al...
متن کاملSingular 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...
متن کاملBoundedness 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...
متن کاملMean Oscillation and Boundedness of Multilinear Integral Operators with General Kernels
As the development of singular integral operators, their commutators and multilinear operators have been well studied (see [3]–[7], [18]–[20]). Let T be the Calderón-Zygmund singular integral operator and b ∈ BMO(R), a classical result of Coifman, Rochberg and Weiss (see [6]) stated that the commutator [b, T ](f) = T (bf)− bT (f) is bounded on L(R) for 1 < p <∞. The purpose of this paper is to ...
متن کامل