Logarithmic sobolev inequalities — A survey

  • Leonard Gross
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 644)


Sobolev Inequality Gauss Measure Number Operator Logarithmic Sobolev Inequality Infinite Dimension 
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  1. [1]
    W. Beckner, Inequalities in Fourier analysis on Rn, Proc. Nat. Acad. Sci. U.S.A. 72(1975), 638–641.MathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    ____, Inequalities in Fourier Analysis, Ann. of Math. 102 (1975), 159–182.MathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    I.B. Birula and J. Mycielski, Uncertainty relations for information entropy in wave mechanics, Commun. in Math. Phys. 44(1975), 129–132.MathSciNetCrossRefGoogle Scholar
  4. [4]
    P.M. Bleher and M.I. Visik, On a class of pseudodifferential operators with an infinite number of variables, and applications. Mat. Sbornik Tom 86(128) (1971), No. 3.Google Scholar
  5. [5]
    H.J. Brascamp and E.H. Lieb, Best constants in Young's inequality, its converse, and its generalization to more than three functions, Princeton preprint 1975.Google Scholar
  6. [6]
    Yu. L. Daletzky, Differential Equations with functional derivatives and stochastic equations for generalized random processes, Dokl. Akad. Nauk SSSR 166 (1966), 1035–1038.MathSciNetGoogle Scholar
  7. [7]
    ____, Infinite dimensional elliptic operators and the corresponding parabolic equations. Uspehi Math. Nauk Vol. 22 No. 4 (136), 3–54.Google Scholar
  8. [8]
    J.P. Eckmann, Hypercontractivity for anharmonic oscillators, J. Funct. Anal. 16(1974), 388–406.MathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    W. Faris, Product spaces and Nelson's inequality, Helv. Phys. Acta, 48(1975) 721–730.MathSciNetGoogle Scholar
  10. [10]
    G. Feissner, Hypercontractive semigroups and Sobolev's inequality, T.A.M.S. 210(1975), 51–62.MathSciNetzbMATHGoogle Scholar
  11. [11]
    J. Glimm, Boson fields with nonlinear self-interaction in two dimensions, Comm. Math. Phys. 8(1968), 12–25.CrossRefzbMATHGoogle Scholar
  12. [12]
    L. Gross, Logarithmic Sobolev inequalities, Amer. J. of Math. 97(1975) 1061–1083.MathSciNetCrossRefzbMATHGoogle Scholar
  13. [13]
    ____, Potential theory on Hilbert space, J. of Funct. Anal. 1(1967), 123–181.MathSciNetCrossRefzbMATHGoogle Scholar
  14. [14]
    E. Nelson, A quartic interaction in two dimensions, in Mathematical Theory of Elementary Particles, 69–73. (R. Goodman and I. Segal, eds.) M.I.T. Press, Cambridge, Mass., 1966.Google Scholar
  15. [15]
    ____, The free Markoff field, J. of Funct. Anal. 12(1973), 211–227.MathSciNetCrossRefzbMATHGoogle Scholar
  16. [16]
    L. Nirenberg, On elliptic partial differential equations, Ann. Scuola Normale Superiore di Pisa, Ser. III, 13(1959), 1–47.MathSciNetzbMATHGoogle Scholar
  17. [17]
    M.A. Piech, Some regularity properties of diffusion processes on Abstract Wiener space, J. of Funct. Anal. 8(1971), 153–172.MathSciNetCrossRefzbMATHGoogle Scholar
  18. [18]
    J. Rosen, Sobolev inequalities for weight spaces and supercontractivity, Trans. A.M.S. 222(1976), 367–376.MathSciNetCrossRefzbMATHGoogle Scholar
  19. [19]
    I.E. Segal, Construction of nonlinear local quantum processes, I, Ann. of Math. 92(1970), 462–481.MathSciNetCrossRefzbMATHGoogle Scholar
  20. [20]
    ____, Construction of nonlinear local quantum processes, II, Inventiones Math., 14(1971), 211–241.CrossRefzbMATHGoogle Scholar
  21. [21]
    B. Simon and R. Hoegh-Krohn, Hypercontractive semi-groups and two dimensional self-coupled Bose Fields, J. Funct. Anal. 9(1972), 121–180.MathSciNetCrossRefzbMATHGoogle Scholar
  22. [22]
    B. Simon, The P(Ø)2 Euclidean (Quantum) field theory, Princeton Univ. Press, Princeton, N.J. (1974).Google Scholar

Copyright information

© Springer-Verlag 1978

Authors and Affiliations

  • Leonard Gross
    • 1
  1. 1.Department of MathematicsCornell UniversityUSA

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