Geodesic
Bilinear operators associated with Schrödinger operators
Chin-Cheng Lin 1   ; Ying-Chieh Lin 1   ; Heping Liu 2   ; Yu Liu 3
1 Department of Mathematics National Central University Chung-Li 320, Taiwan
2 LMAM, School of Mathematical Sciences Peking University Beijing 100871, China
3 School of Mathematics and Physics University of Science and Technology Beijing Beijing 100083, China
Studia Mathematica, Tome 205 (2011) no. 3, pp. 281-295 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/sm205-3-4
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

Chin-Cheng Lin  1   ; Ying-Chieh Lin  1   ; Heping Liu  2   ; Yu Liu  3

1 Department of Mathematics National Central University Chung-Li 320, Taiwan
2 LMAM, School of Mathematical Sciences Peking University Beijing 100871, China
3 School of Mathematics and Physics University of Science and Technology Beijing Beijing 100083, China 
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     title = {Bilinear operators associated with {Schr\"odinger} operators},
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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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