no. 7-8
Partial Differential Equations/Functional Analysis
On an extension of a bilinear functional on Lp(Rd)⊗E to a Bochner space with an application to velocity averaging
[Sur une extension dʼune fonctionnelle bilinéaire sur Lp(Rd)⊗E aux espaces du Bochner avec une application sur la moyennisation en vitesse]
Présenté par : Yves Meyer
Lazar, Martin1, 2 ; Mitrović, Darko3
1 University of Dubrovnik, Department of Electrical Engineering and Computing, Dubrovnik, Croatia
2 BCAM – Basque Center for Applied Mathematics, Bilbao, Spain
3 University of Montenegro, Faculty of Mathematics, Podgorica, Montenegro
Comptes Rendus. Mathématique, Tome 351 (2013) no. 7-8, pp. 261-264

We examine necessary and sufficient conditions under which a continuous bilinear functional B on Lp(Rd)⊗E, p>1, E being a separable Banach space, can be continuously extended to a linear functional on Lp(Rd;E). The extension enables a generalisation of the H-distribution concept, allowing us to obtain a (heterogeneous) velocity averaging result in the Lp framework for any p>1.

Nous examinons les conditions nécessaires et suffisantes pour quʼune fonctionelle bilinéaire continue sur Lp(Rd)⊗E, p>1, E étant un espace de Banach séparable, peut être étendue à une fonctionnelle linaire sur Lp(Rd;E). Lʼextension permet une généralisation de lʼH-distribution, qui fournit lʼamélioration dʼun résultat de moyennisation en vitesse (hétèrogène) sur le cadre Lp pour tout p>1.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2013.04.013

Lazar, Martin 1, 2 ; Mitrović, Darko 3

1 University of Dubrovnik, Department of Electrical Engineering and Computing, Dubrovnik, Croatia
2 BCAM – Basque Center for Applied Mathematics, Bilbao, Spain
3 University of Montenegro, Faculty of Mathematics, Podgorica, Montenegro 
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     title = {On an extension of a bilinear functional on $ {\mathrm{L}}^{p}({\mathbf{R}}^{d})\otimes E$ to a {Bochner} space with an application to velocity averaging},
     journal = {Comptes Rendus. Math\'ematique},
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Lazar, Martin; Mitrović, Darko. On an extension of a bilinear functional on $ {\mathrm{L}}^{p}({\mathbf{R}}^{d})\otimes E$ to a Bochner space with an application to velocity averaging. Comptes Rendus. Mathématique, Tome 351 (2013) no. 7-8, pp. 261-264. doi: 10.1016/j.crma.2013.04.013

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