engleski

On an extension of a bilinear functional on $L^p(R^d) x E$ to a Bochner space with an application to velocity averaging

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

velocity averaging; H-distributions

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