Glasnik Matematicki, Vol. 52, No. 1 (2017), 115-130.

ON A NEW CLASS OF FUNCTIONAL SPACES WITH APPLICATION TO THE VELOCITY AVERAGING

Martin Lazar and Darko Mitrović

Faculty of Mathematics and Natural Sciences, University of Montenegro, Cetinjski put bb, 81000 Podgorica, Montenegro
e-mail: darkom@ac.me

Abstract.   We introduce a new family of functional spaces which incorporate Bochner spaces L^p(R^m; E), with E being an appropriate Banach space, and to which we extend the H-distributions. We use the developed theory to prove a general version of the velocity averaging lemma in a heterogeneous L^p, p ≤ 2 setting.

2010 Mathematics Subject Classification.   35A27, 46B50, 47G30.

Key words and phrases.   H-distributions, velocity averaging, non-degeneracy condition.

DOI: 10.3336/gm.52.1.09

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