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• # Artykuł - szczegóły

## Studia Mathematica

2011 | 205 | 3 | 281-295

## Bilinear operators associated with Schrödinger operators

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.

281-295

wydano
2011

### Twórcy

autor
• Department of Mathematics, National Central University, Chung-Li 320, Taiwan
autor
• Department of Mathematics, National Central University, Chung-Li 320, Taiwan
autor
• LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, China
autor
• School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China