Bilinear operators associated with Schrödinger operators

Chin-Cheng Lin, et al. "Bilinear operators associated with Schrödinger operators." Studia Mathematica 205.3 (2011): 281-295. <http://eudml.org/doc/285630>.

@article{Chin2011,
abstract = {Let L = -Δ + V be a Schrödinger operator in $ℝ^\{d\}$ and $H¹_L(ℝ^\{d\})$ be the Hardy type space associated to L. We investigate the bilinear operators T⁺ and T¯ defined by $T^\{±\}(f,g)(x) = (T₁f)(x)(T₂g)(x) ± (T₂f)(x)(T₁g)(x)$, where T₁ and T₂ are Calderón-Zygmund operators related to L. Under some general conditions, we prove that either T⁺ or T¯ is bounded from $L^\{p\}(ℝ^\{d\}) × L^\{q\}(ℝ^\{d\})$ to $H¹_L(ℝ^\{d\})$ for 1 < p,q < ∞ 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.},
author = {Chin-Cheng Lin, Ying-Chieh Lin, Heping Liu, Yu Liu},
journal = {Studia Mathematica},
keywords = {bilinear operators; Hardy spaces; Riesz transforms; Schrödinger operators},
language = {eng},
number = {3},
pages = {281-295},
title = {Bilinear operators associated with Schrödinger operators},
url = {http://eudml.org/doc/285630},
volume = {205},
year = {2011},
}

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
VL - 205
IS - 3
SP - 281
EP - 295
AB - Let L = -Δ + V be a Schrödinger operator in $ℝ^{d}$ and $H¹_L(ℝ^{d})$ be the Hardy type space associated to L. We investigate the bilinear operators T⁺ and T¯ defined by $T^{±}(f,g)(x) = (T₁f)(x)(T₂g)(x) ± (T₂f)(x)(T₁g)(x)$, where T₁ and T₂ are Calderón-Zygmund operators related to L. Under some general conditions, we prove that either T⁺ or T¯ is bounded from $L^{p}(ℝ^{d}) × L^{q}(ℝ^{d})$ to $H¹_L(ℝ^{d})$ for 1 < p,q < ∞ 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.
LA - eng
KW - bilinear operators; Hardy spaces; Riesz transforms; Schrödinger operators
UR - http://eudml.org/doc/285630
ER -