no. 3-4
L p regularity of velocity averages
Annales de l'I.H.P. Analyse non linéaire, Tome 8 (1991) no. 3-4, pp. 271-287. 
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     title = {$L^p$ regularity of velocity averages},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {271--287},
     publisher = {Gauthier-Villars},
     volume = {8},
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     year = {1991},
     mrnumber = {1127927},
     zbl = {0763.35014},
     language = {en},
     url = {http://archive.numdam.org/item/AIHPC_1991__8_3-4_271_0/}
}
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Diperna, R. J.; Lions, P. L.; Meyer, Y. $L^p$ regularity of velocity averages. Annales de l'I.H.P. Analyse non linéaire, Tome 8 (1991) no. 3-4, pp. 271-287. http://archive.numdam.org/item/AIHPC_1991__8_3-4_271_0/

[1] V.I. Agoshkov, Spaces of Functions with Differential-Difference Characteristics and Smoothness of Solutions of the Transport Equation, Soviet Math. Dokl., Vol. 29, 1984, pp. 662-666. | MR | Zbl

[2] V.I. Agoshkov, Functional spaces H p 1 ( Ω × D ) , H p t + α , k ( Ω × D ) ) and solvability conditions of boundary problems for transport equations, Preprint.

[3] J. Bergh and J. Löfstrom, Interpolation spaces. An introduction. Springer, Berlin, 1976. | MR | Zbl

[4] S.Y.A. Chang and R. Fefferman, Some Recent Developments in Fourier Analysis and H p -Theory on Product Domains, Bull. Amer. Math. Soc., Vol. 12, 1985, pp. 1-43. | MR | Zbl

[5] S.Y.A. Chang and R. Fefferman, The Calderon-Zygmund Decompositions on Product Domains, Amer. J. Math., Vol. 104, 1982, pp. 445-468. | MR | Zbl

[6] L. Desvillettes, Personnal communication and work in preparation.

[7] R.J. Diperna and P.L. Lions, On the Cauchy Problem for Boltzmann Equations: Global Existence and Weak Stability, Ann. Math., Vol. 130, 1989, pp. 321-366; see also C. R. Acad. Sci. Paris, T. 306, Series I, 1988, pp. 343-346. | MR | Zbl

[8] R.J. Diperna and P.L. Lions, Global Solutions of Boltzmann Equations and the Entropy Inequality, Arch. Rat. Mech. Anal., 1990; see also in Séminaire E.D.P. 1987- 1988, École Polytechnique, Palaiseau, 1989. | Numdam | MR | Zbl

[9] R.J. Diperna and P.L. Lions, Global Weak Solutions of Vlasov-Maxwell Systems, Comm. Pure Appl. Math., Vol. XLII, 1989, pp. 729-757. | MR | Zbl

[10] R.J. Diperna and P.L. Lions, Work in preparation, see also C. R. Acad. Sci. Paris, R. 307, Series I, 1988, pp. 655-658. | MR | Zbl

[11] R.J. Diperna and P.L. Lions, Work in preparation, see also Global Weak Solutions of Kinetic Equations, Seminario Matematico, Torino, 1990 (to appear). | MR

[12] P. Gérard, Moyennisation et régularité deux-microlocale. Preprint. | MR

[13] P. Gérard, Moyennes de solutions d'équations aux dérivées partielles. In Séminaire E.D.P. 1986-1987, École Polytechnique, Palaiseau, 1988. | Numdam | Zbl

[14] P. Gérard and F. Golse, Personnal communication.

[15] F. Golse, P.L. Lions, B. Perthame and R. Sentis, Regularity of the Moments of the Solution of a Transport Equation, J. Funct. Anal., Vol. 76, 1988, pp. 110-125. | MR | Zbl

[16] F. Golse, B. Perthame and R. Sentis, Un résultat de compacité pour les équations de transport et applications au calcul de la limite de la valeur propre principale d'un opérateur de transport, C. R. Acad. Sci. Paris, T. 301, Series, 1985, pp. 341-344. | MR | Zbl

[17] L. Hörmander, Estimates for Translation-Invariant Operators in L p Spaces, Acata Math., Vol. 104, 1960, pp. 93-139. | MR | Zbl

[18] K.C. Lin, Hp interpolation on the Bi-Disc, Preprint.

[19] J.E. Littlewood and R. Paley, Theorems on Fourier Series and Power Series (II), Proc. London Math. Soc., Vol. 42, 1937, pp. 52-89. | JFM

[20] S.G. Mihlin, Fourier Integrals and Multiple Singular Integrals, Vestnik Leningrad Univ. Ser. Mat., Vol. 12, 1957, pp. 143-145 (in Russian). | MR | Zbl

[21] J. Peetre, Sur les espaces de Becov, C. R. Acad. Sci. Paris, T. 264, Series I, 1967, pp. 281-283. | MR | Zbl

[22] E.M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, Princeton, 1970. | MR | Zbl