References
Adams R. A. andClarke, F. H., Gross’ logarithmic Sobolev inequality: a simple proof.Amer. J. Math. 101 (1979) 1265–1270.
Baernstein A. andTaylor B. A., Spherical rearrangements, subharmonic functions, and *-functions inn-space.Duke Math. J. 43 (1976), 245–268.
Beckner, W., Inequalities in Fourier analysis.Ann. Math. 102 (1975), 159–182.
Bonami, A., Étude des coefficients de Fourier des fonctions deL p(G).Ann. Inst. Fourier 20:2 (1970), 335–402.
Borell C., Convexity in Gauss space. Les aspects statistiques et les aspects physiques des processus gaussins. S:t Flour 1980 (to appear).
Brascamp H. J. andLieb, E. H., Best constants in Young’s inequality, its converse, and its generalization to more than three functions.Adv. Math. 20 (1976), 151–173.
Carmona, R., Regularity properties of Schrödinger and Dirichlet semigroups.J. Functional Anal. 33 (1979), 259–296.
Coifman, M., Cwikel, M., Rochberg, R., Sagher, Y. andWeiss, G., Complex interpolation of families of spaces.Proceedings of Symposia in Pure Mathematics 35:2 (1979), 269–282.
Gross, L., Logarithmic Sobolev inequalities.Amer. J. Math. 97 (1975), 1061–1083.
Nelson, E., The free Markov field.J. Functional Anal. 12 (1973), 211–227.
Neveu, J., Sur l’espérance conditionnelle par rapport à un mouvement brownien.Ann. Inst. H. Poincaré B12 (1976), 105–109.
Peetre, J., A class of kernels related to the inequalities of Beckner and Nelson. “A tribute to Åke Pleijel”, Uppsala 1980, 171–210.
Segal, I., Construction of non-linear local quantum processes I.Ann. Math. 92 (1970), 462–481.
Simon, B., A remark on Nelson’s best hypercontractive estimates.Proc. Amer. Math. Soc. 55 (1976), 376–378.
Stein, E. M., andWeiss, G., Introduction to Fourier Analysis on Euclidean spaces. Princeton 1971.
Weissler, F. B., Two-point inequalities, the Hermite semigroup and the Gauss-Weierstrass’ semigroup.J. Functional Anal. 32 (1979), 102–121.
Weissler, F. B., Logarithmic Sobolev inequalities and hypercontractive estimates on the circle.J. Functional Anal. 37 (1980), 218–234.
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Janson, S. On hypercontractivity for multipliers on orthogonal polynomials. Ark. Mat. 21, 97–110 (1983). https://doi.org/10.1007/BF02384302
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DOI: https://doi.org/10.1007/BF02384302