Bilinear operators associated with Schrödinger operators

• Autorzy: Chin-Cheng Lin , Ying-Chieh Lin , Heping Liu , Yu Liu
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 35J10: Schr\"odinger operator
• 42A20: Convergence and absolute convergence of Fourier and trigonometric series

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2011
• Tom: 205
• Numer: 3
• Strony: 281-295

Daty

wydano

2011

Twórcy

autor

Chin-Cheng Lin

• Department of Mathematics, National Central University, Chung-Li 320, Taiwan

autor

Ying-Chieh Lin

• Department of Mathematics, National Central University, Chung-Li 320, Taiwan

autor

Heping Liu

• LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, China

autor

Yu Liu

• School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China

Identyfikatory

DOI

10.4064/sm205-3-4