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

**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

**References:**

- N. Antonić and D. Mitrović,
, Abstr. Appl. Anal.*H*-distributions: an extension of*H*-measures to an*L*-^{p}*L*setting^{q}**2011**, Art. ID 901084, 12 pp.

MathSciNet CrossRef - P. Gérard,
*Microlocal defect measures*, Comm. Partial Differential Equations**16**(1991), 1761-1794.

MathSciNet CrossRef - F. Golse, P.-L. Lions, B. Perthame and R. Sentis,
*Regularity of the moments of the solution of a transport equation*, J. Funct. Anal.**76**(1988), 110-125.

MathSciNet CrossRef - L. Grafakos, Classical Fourier analysis,
Springer, New York, 2008.

MathSciNet - M. Lazar and D. Mitrović,
*The velocity averaging for a heterogeneous heat type equation*, Math. Commun.**16**(2011), 271-282.

MathSciNet - M. Lazar and D. Mitrović,
*Velocity averaging - a general framework*, Dyn. of Partial Differ. Equ.**9**(2012), 239-260.

MathSciNet CrossRef - M. Lazar and D. Mitrović,
*On an extension of a bilinear functional on*, C. R. Math. Acad. Sci. Paris*L*to a Bochner space with an application to velocity averaging^{p}(R^{d}) × E**351**(2013), 261-264.

MathSciNet CrossRef - M. Lazar and D. Mitrović,
*On the velocity averaging for equations with optimal heterogeneous rough coefficients*, preprint available on arXiv,`http://arxiv.org/pdf/1310.4285.pdf`. - E. Yu. Panov,
*Ultra-parabolic equations with rough coefficients. Entropy solutions and strong precompactness property*, J. Math. Sci. (N.Y.)**159**(2009), 180-228.

MathSciNet CrossRef - B. Perthame and P.E. Souganidis,
*A limiting case for velocity averaging*, Ann. Sci. École Norm. Sup. (4)**31**(1998), 591-598.

MathSciNet CrossRef - E. Tadmor and T. Tao,
*Velocity averaging, kinetic formulations, and regularizing effects in quasi-linear PDEs*, Comm. Pure Appl. Math.**60**(2007), 1488-1521.

MathSciNet CrossRef - L. Tartar,
, Proc. Roy. Soc. Edinburgh Sect. A*H*-measures, a new approach for studying homogenisation, oscillation and concentration effects in partial differential equations**115**(1990), 193-230.

MathSciNet CrossRef - L. Tartar, The general theory of homogenization: a personalized introduction,
Springer-Verlag, Berlin, 2009.

MathSciNet CrossRef -
L. R. Volevich and B. P. Paneyakh,
*Certain spaces of generalized functions and embedding theorems*, Russ. Math. Surv.**20**(1965), 1-73.

CrossRef -
K. Yosida, Functional analysis,
Springer-Verlag, Berlin-New York, 1980.

MathSciNet