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 to . One-sided singular integrals, like the differential transform operator, are considered as well. We also provide applications to Fourier multipliers and homogeneous singular integrals.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm195-2-5,
author = {Mar\'\i a Lorente and Jos\'e Mar\'\i a Martell and Carlos P\'erez and Mar\'\i a Silvina Riveros},
title = {Generalized H\"ormander conditions and weighted endpoint estimates},
journal = {Studia Mathematica},
volume = {192},
year = {2009},
pages = {157-192},
zbl = {1179.42013},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm195-2-5}
}
María Lorente; José María Martell; Carlos Pérez; María Silvina Riveros. Generalized Hörmander conditions and weighted endpoint estimates. Studia Mathematica, Tome 192 (2009) pp. 157-192. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm195-2-5/