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
Comptes Rendus. Mathématique, Volume 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.

Received:
Accepted:
Published online:
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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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, Volume 351 (2013) no. 7-8, pp. 261-264. doi : 10.1016/j.crma.2013.04.013. http://www.numdam.org/articles/10.1016/j.crma.2013.04.013/

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