Characterization of Lipschitz functions via the commutators of multilinear fractional integral operators in variable Lebesgue spaces

Commutators of integral operators with variable kernels on Hardy spaces

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...

Commutators with Lipschitz Functions and Nonintegral Operators

Let T be a singular nonintegral operator; that is, it does not have an integral representation by a kernel with size estimates, even rough. In this paper, we consider the boundedness of commutators with T and Lipschitz functions. Applications include spectral multipliers of self-adjoint, positive operators, Riesz transforms of second-order divergence form operators, and fractional power of elli...

Lipschitz Estimates for Multilinear Commutator of Pseudo-differential Operators

As the development of singular integral operators, their commutators and multilinear operators have been well studied (see [4, 5, 6, 7, 8, 9, 10]). In [4, 5, 6, 7, 8, 9, 10], the authors prove that the commutators and multilinear operators generated by the singular integral operators and BMO functions are bounded on L(R) for 1 < p <∞; Chanillo (see [2]) proves a similar result when singular int...

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

Commutators of Multilinear Singular Integral Operators on Non-homogeneous Metric Measure Spaces

Abstract. Let (X, d, μ) be a metric measure space satisfying both the geometrically doubling and the upper doubling measure conditions, which is called nonhomogeneous metric measure space. In this paper, via a sharp maximal operator, the boundedness of commutators generated by multilinear singular integral with RBMO(μ) function on non-homogeneous metric measure spaces in m-multiple Lebesgue spa...