Generalized Hörmander conditions and weighted endpoint estimates
Volume 195 / 2009
Studia Mathematica 195 (2009), 157-192
MSC: 42B20, 42B25.
DOI: 10.4064/sm195-2-5
Abstract
We consider two-weight estimates for singular integral operators and their commutators with bounded mean oscillation functions. Hörmander type conditions in the scale of Orlicz spaces are assumed on the kernels. We prove weighted weak-type estimates for pairs of weights $(u, Su)$ where $u$ is an arbitrary nonnegative function and $S$ is a maximal operator depending on the smoothness of the kernel. We also obtain sufficient conditions on a pair of weights $(u,v)$ for the operators to be bounded from $L^p(v)$ to $L^{p,\infty }(u)$. One-sided singular integrals, like the differential transform operator, are considered as well. We also provide applications to Fourier multipliers and homogeneous singular integrals.
