Generalized Hörmander conditions and
weighted endpoint estimates
Studia Mathematica, Tome 195 (2009) no. 2, pp. 157-192
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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.
Keywords:
consider two weight estimates singular integral operators their commutators bounded mean oscillation functions rmander type conditions scale orlicz spaces assumed kernels prove weighted weak type estimates pairs weights where arbitrary nonnegative function maximal operator depending smoothness kernel obtain sufficient conditions pair weights operators bounded infty one sided singular integrals differential transform operator considered provide applications fourier multipliers homogeneous singular integrals
Affiliations des auteurs :
María Lorente 1 ; José María Martell 2 ; Carlos Pérez 3 ; María Silvina Riveros 4
@article{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},
pages = {157--192},
publisher = {mathdoc},
volume = {195},
number = {2},
year = {2009},
doi = {10.4064/sm195-2-5},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm195-2-5/}
}
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 SP - 157 EP - 192 VL - 195 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4064/sm195-2-5/ DO - 10.4064/sm195-2-5 LA - en ID - 10_4064_sm195_2_5 ER -
%0 Journal Article %A María Lorente %A José María Martell %A Carlos Pérez %A María Silvina Riveros %T Generalized Hörmander conditions and weighted endpoint estimates %J Studia Mathematica %D 2009 %P 157-192 %V 195 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4064/sm195-2-5/ %R 10.4064/sm195-2-5 %G en %F 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 195 (2009) no. 2, pp. 157-192. doi: 10.4064/sm195-2-5
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