L p regularity of velocity averages
Diperna, R. J. ; Lions, P. L. ; Meyer, Y.
Annales de l'I.H.P. Analyse non linéaire, Tome 8 (1991), p. 271-287 / Harvested from Numdam
@article{AIHPC_1991__8_3-4_271_0,
     author = {Diperna, R. J. and Lions, Pierre-Louis and Meyer, Yves},
     title = {$L^p$ regularity of velocity averages},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {8},
     year = {1991},
     pages = {271-287},
     mrnumber = {1127927},
     zbl = {0763.35014},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_1991__8_3-4_271_0}
}
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) pp. 271-287. http://gdmltest.u-ga.fr/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 753365 | Zbl 0599.35009

[2] V.I. Agoshkov, Functional spaces H1p (Ω × D), Ht+α,kp (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 482275 | Zbl 0344.46071

[4] S.Y.A. Chang and R. Fefferman, Some Recent Developments in Fourier Analysis and Hp-Theory on Product Domains, Bull. Amer. Math. Soc., Vol. 12, 1985, pp. 1-43. | MR 766959 | Zbl 0557.42007

[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 658542 | Zbl 0513.42019

[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 1014927 | Zbl 0698.45010

[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 1018178 | Zbl 0724.45011

[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 1003433 | Zbl 0698.35128

[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 967806 | Zbl 0682.35022

[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 1101105

[12] P. Gérard, Moyennisation et régularité deux-microlocale. Preprint. | MR 1042388

[13] P. Gérard, Moyennes de solutions d'équations aux dérivées partielles. In Séminaire E.D.P. 1986-1987, École Polytechnique, Palaiseau, 1988. | Numdam | Zbl 0657.35020

[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 923047 | Zbl 0652.47031

[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 808622 | Zbl 0591.45007

[17] L. Hörmander, Estimates for Translation-Invariant Operators in Lp Spaces, Acata Math., Vol. 104, 1960, pp. 93-139. | MR 121655 | Zbl 0093.11402

[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 63.0214.03

[20] S.G. Mihlin, Fourier Integrals and Multiple Singular Integrals, Vestnik Leningrad Univ. Ser. Mat., Vol. 12, 1957, pp. 143-145 (in Russian). | MR 88603 | Zbl 0092.31701

[21] J. Peetre, Sur les espaces de Becov, C. R. Acad. Sci. Paris, T. 264, Series I, 1967, pp. 281-283. | MR 218887 | Zbl 0145.16206

[22] E.M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, Princeton, 1970. | MR 290095 | Zbl 0207.13501