A note on weighted bounds for singular operators with nonsmooth kernels
Volume 236 / 2017
Studia Mathematica 236 (2017), 245-269
MSC: Primary 42B20; Secondary 42B25.
DOI: 10.4064/sm8409-9-2016
Published online: 20 January 2017
Abstract
Let $T$ be a multilinear {integral} operator which is bounded on certain products of Lebesgue spaces on $\mathbb R^n$. We assume that its associated kernel satisfies some mild regularity condition which is weaker than the usual Hölder continuity of kernels of multilinear Calderón–Zygmund singular integral operators. In this paper, given a suitable multiple weight $\vec{w}$, we obtain a bound for the weighted norm of $T$ in terms of $\vec{w}$. As applications, we obtain new weighted bounds for certain singular integral operators such as linear and multilinear Fourier multipliers and the Riesz transforms associated to Schrödinger operators on $\mathbb {R}^n$.
