Pomiędzy Poincarém a Sobolewem

• Autorzy: Latała Rafał

Identyfikatory

DOI

10.14708/wm.v40i01.4973

• Języki publikacji: PL
• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Wiadomości Matematyczne
• Rocznik: 2004
• Tom: T. 40, Nr 1
• Strony: 67--76
• Opis fizyczny: Bibliogr. 17 poz.

Twórcy

autor

Latała Rafał

• University of Warsaw: Warsaw, PL

• https://orcid.org/0000-0002-2609-2869

Bibliografia

• [1] C. Ané, S. Blachère, D. Chafaï, P. Fougères, I. Gentil, F. Mairieu, C. Roberto, G. Scheffer, Sur les inégalités de Sobolev logarithmiques, Panoramas et Synthèses 10, Société Mathématique de France, Paris 2000.
• [2] S. Aida, D. Strоосk, Moment estimates derived from Poincaré and logarithmic Sobolev inequalities, Math. Res. Lett. 1 (1994), 75-86.
• [3] A. Arnold, P. Markowich, G. Toscani, A. Unterreiter, On convex Sobolev inequalities and the rate of convergence to equilibrium for Fokker-Planck type inequalities, Commm. Partial Differential Equations 26 (2001), 43-100.
• [4] K. Ball, F. Вarthe, A. Naor, Entropy jumps in the presence of a spectral gap, Duke Math. J. 119 (2003), 41-63.
• [5] F. Barthe, C. Roberto, Sobolev inequalities for probability measures on the real line, Studia Math. 159 (2003), 481-497.
• [6] S. Bobkov, A. Koldobsky, On the central limit property of convex bodies, w Geometric aspects of functional analysis, Lecture Notes in Math. 1807, 44-52, Springer, Berlin 2003.
• [7] С. Воrell, Convex measures on locally convex spaces, Ark. Math. 12 (1974), 239- 252.
• [8] S. Boucheron, O. Bousquet, G. Lugosi, P. Massart, Moment inequalities for functions of independent random variables, preprint.
• [9] S. G. Bobkov, F. Götze, Exponential integrability and transportation cost related to logarithmic Sobolev inequalities, J. Funct. Anal. 163 (1999), 1-28.
• [10] A. Guionnet, B. Zegarlinski, Lectures on logarithmic Sobolev inequalities, Séminaire de Probabilités XXXVI, Lecture Notes in Math. 1801, 1-134, Springer, Berlin 2003.
• [11] B. Helffer, Semiclassical analysis, Witten Laplacians, and statistical mechanics, Ser. Partial Differential Equation Appl. 1, World Sci., River Edge, NJ, 2002.
• [12] R. Kannan, L. Lovász, M. Simonovits, Isoperimetric problems for convex bodies and a localization lemma, Discrete and Comput. Geom. 13 (1995), 541-559.
• [13] R. Latała, K. Oleszkiewicz, Between Sobolev and Poincaré, w: Geometric aspects of functional analysis, Lecture Notes in Math. 1745, 147-168, Springer, Berlin 2000.
• [14] M. Ledoux, The concentration of measure phenomenon, Americal Mathematical Society, Providence, RI, 2001.
• [15] K. Oleszkiewicz, Własność hiperkontrakcji i uogólnione nierówności Chinczyna-Kahane’a, praca magisterska, Uniwersytet Warszawski 1994.
• [16] G. Royer, Une initiation aux inégalités de Sobolev logaritmiques, Cours Spécialisés 5, Société Mathématique de France, Paris 1999.
• [17] С. Villani, Topics in Optimal Transportation, Graduate Studies in Mathematics 58, American Mathematical Society, Providence, RI, 2003.