Generalized Hörmander's conditions and weighted endpoint estimates

M.LORENTE, J.M. MARTELL, C. PÉREZ, M.S. RIVEROS

STUDIA MATHEMATICA

Año: 2009

0039-3223

We consider two-weight estimates for singular integral operators and their commutators with bounded mean oscillation functions. Hörmander´s 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, as the differential transform operator, are under study. We also provide applications to Fourier multipliers and homogeneous singular integrals.