Bilinear operators associated with Schrödinger operators

Chin-Cheng Lin; Ying-Chieh Lin; Heping Liu; Yu Liu

Chin-Cheng Lin ; Ying-Chieh Lin ; Heping Liu ; Yu Liu

Studia Mathematica, Tome 204 (2011), p. 281-295 / Harvested from The Polish Digital Mathematics Library

Résumé

Let L = -Δ + V be a Schrödinger operator in $ℝ^{d}$ and $H ¹_{L} (ℝ^{d})$ be the Hardy type space associated to L. We investigate the bilinear operators T⁺ and T¯ defined by $T^{\pm} (f, g) (x) = (T ₁ f) (x) (T ₂ g) (x) \pm (T ₂ f) (x) (T ₁ g) (x)$ , 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 $L^{p} (ℝ^{d}) \times L^{q} (ℝ^{d})$ to $H ¹_{L} (ℝ^{d})$ 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.

Publié le : 2011-01-01

Zbl 1229.42010

EUDML-ID : urn:eudml:doc:285630

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     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},
     volume = {204},
     year = {2011},
     pages = {281-295},
     zbl = {1229.42010},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm205-3-4}
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Chin-Cheng Lin; Ying-Chieh Lin; Heping Liu; Yu Liu. Bilinear operators associated with Schrödinger operators. Studia Mathematica, Tome 204 (2011) pp. 281-295. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm205-3-4/