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Logarithmic Sobolev inequalities for the heat-diffusion semigroup. (English) Zbl 0376.47019

##### MSC:
 47D03 Groups and semigroups of linear operators 46E30 Spaces of measurable functions ($$L^p$$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
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##### References:
 [1] William Beckner, Inequalities in Fourier analysis, Ann. of Math. (2) 102 (1975), no. 1, 159 – 182. · Zbl 0338.42017 [2] Herm Jan Brascamp and Elliott H. Lieb, Best constants in Young’s inequality, its converse, and its generalization to more than three functions, Advances in Math. 20 (1976), no. 2, 151 – 173. · Zbl 0339.26020 [3] Leonard Gross, Logarithmic Sobolev inequalities, Amer. J. Math. 97 (1975), no. 4, 1061 – 1083. · Zbl 0318.46049 [4] S. Mazur, Über schwache Konvergence in den Räumen ($${L^p}$$), Studia Math. 4 (1933), 128-133. · JFM 59.1076.01 [5] Edward Nelson, The free Markoff field, J. Functional Analysis 12 (1973), 211 – 227. · Zbl 0273.60079 [6] H. L. Royden, Real analysis, The Macmillan Co., New York; Collier-Macmillan Ltd., London, 1963. · Zbl 0121.05501
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