Generalized Hörmander conditions and weighted endpoint estimates

María Lorente, et al. "Generalized Hörmander conditions and weighted endpoint estimates." Studia Mathematica 195.2 (2009): 157-192. <http://eudml.org/doc/285344>.

@article{MaríaLorente2009,
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 $L^\{p,∞\}(u)$. One-sided singular integrals, like the differential transform operator, are considered as well. We also provide applications to Fourier multipliers and homogeneous singular integrals.},
author = {María Lorente, José María Martell, Carlos Pérez, María Silvina Riveros},
journal = {Studia Mathematica},
keywords = {singular integral; Hörmander condition; Muckenhoupt weight; Young function; commutator; BMO},
language = {eng},
number = {2},
pages = {157-192},
title = {Generalized Hörmander conditions and weighted endpoint estimates},
url = {http://eudml.org/doc/285344},
volume = {195},
year = {2009},
}

TY - JOUR
AU - María Lorente
AU - José María Martell
AU - Carlos Pérez
AU - María Silvina Riveros
TI - Generalized Hörmander conditions and weighted endpoint estimates
JO - Studia Mathematica
PY - 2009
VL - 195
IS - 2
SP - 157
EP - 192
AB - 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 $L^{p,∞}(u)$. One-sided singular integrals, like the differential transform operator, are considered as well. We also provide applications to Fourier multipliers and homogeneous singular integrals.
LA - eng
KW - singular integral; Hörmander condition; Muckenhoupt weight; Young function; commutator; BMO
UR - http://eudml.org/doc/285344
ER -