Comptes Rendus
Harmonic Analysis/Functional Analysis
Bellman function and bilinear embedding theorem for Schrödinger-type operators
[Fonction de Bellman et le plongement bilinéaire pour des opérateurs de Schrödinger]
Comptes Rendus. Mathématique, Volume 347 (2009) no. 9-10, pp. 537-540.

On considère un théorème de plongement bilinéaire pour une classe des opérateurs de Schrödinger sur Lp. Le résultat ne depend pas de dimension et il est p-linéaire. On fait une esquisse de la démonstration basée sur trois observations concernant la fonction de Bellman spécifique.

We discuss bilinear embedding theorems for a certain class of Schrödinger operators on Lp. The obtained estimates are dimension-free and linear in p. We outline a uniform proof of the theorem which relies on establishing three crucial properties of the concrete Bellman function we consider.

Reçu le :
Accepté le :
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DOI : 10.1016/j.crma.2009.02.004

Oliver Dragičević 1 ; Alexander Volberg 2, 3

1 Faculty of Mathematics and Physics, University of Ljubljana, and Institute of Mathematics, Physics and Mechanics, Jadranska 19, SI-1000 Ljubljana, Slovenia
2 Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA
3 School of Mathematics, University of Edinburgh, Edinburgh EH9 3JZ, UK
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     author = {Oliver Dragi\v{c}evi\'c and Alexander Volberg},
     title = {Bellman function and bilinear embedding theorem for {Schr\"odinger-type} operators},
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     pages = {537--540},
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Oliver Dragičević; Alexander Volberg. Bellman function and bilinear embedding theorem for Schrödinger-type operators. Comptes Rendus. Mathématique, Volume 347 (2009) no. 9-10, pp. 537-540. doi : 10.1016/j.crma.2009.02.004. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.02.004/

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