Bilinear operators associated with Schrödinger operators
Studia Mathematica, Tome 205 (2011) no. 3, pp. 281-295
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
Let $L=-\Delta+V$ be a Schrödinger operator in $\Bbb R^d$ and
$H^1_L(\Bbb R^d)$ be the Hardy type space associated to $L$.
We investigate the bilinear operators $T^+$ and $T^-$ defined by
$$T^{\pm}(f,g)(x)=(T_1f)(x)(T_2g)(x)\pm(T_2f)(x)(T_1g)(x),$$
where $T_1$ and $T_2$ are Calderón–Zygmund operators related to $L$.
Under some general conditions, we prove that either $T^+$ or $T^-$ is
bounded from $L^p(\Bbb R^d)\times L^q(\Bbb R^d)$ to $H^1_L(\Bbb
R^d)$ for $1 p,q \infty$ with ${1}/{p}+{1}/{q}=1$.
Several examples satisfying these conditions are given. We also give a
counterexample for which the classical Hardy space estimate fails.
Keywords:
delta schr dinger operator bbb bbb hardy type space associated investigate bilinear operators defined where calder zygmund operators related under general conditions prove either bounded bbb times bbb bbb infty several examples satisfying these conditions given counterexample which classical hardy space estimate fails
Affiliations des auteurs :
Chin-Cheng Lin 1 ; Ying-Chieh Lin 1 ; Heping Liu 2 ; Yu Liu 3
@article{10_4064_sm205_3_4,
author = {Chin-Cheng Lin and Ying-Chieh Lin and Heping Liu and Yu Liu},
title = {Bilinear operators associated with {Schr\"odinger} operators},
journal = {Studia Mathematica},
pages = {281--295},
publisher = {mathdoc},
volume = {205},
number = {3},
year = {2011},
doi = {10.4064/sm205-3-4},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm205-3-4/}
}
TY - JOUR AU - Chin-Cheng Lin AU - Ying-Chieh Lin AU - Heping Liu AU - Yu Liu TI - Bilinear operators associated with Schrödinger operators JO - Studia Mathematica PY - 2011 SP - 281 EP - 295 VL - 205 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4064/sm205-3-4/ DO - 10.4064/sm205-3-4 LA - en ID - 10_4064_sm205_3_4 ER -
%0 Journal Article %A Chin-Cheng Lin %A Ying-Chieh Lin %A Heping Liu %A Yu Liu %T Bilinear operators associated with Schrödinger operators %J Studia Mathematica %D 2011 %P 281-295 %V 205 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4064/sm205-3-4/ %R 10.4064/sm205-3-4 %G en %F 10_4064_sm205_3_4
Chin-Cheng Lin; Ying-Chieh Lin; Heping Liu; Yu Liu. Bilinear operators associated with Schrödinger operators. Studia Mathematica, Tome 205 (2011) no. 3, pp. 281-295. doi: 10.4064/sm205-3-4
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