Logarithmic Sobolev inequalities and hypercontractive estimates on the circle.(English)Zbl 0463.46024

MSC:

 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems 46E30 Spaces of measurable functions ($$L^p$$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 47D03 Groups and semigroups of linear operators

Zbl 0338.42017
Full Text:

References:

 [1] {\scR. A. Adams and F. H. Clarke}, preprint, 1978. [2] Beckner, W, Inequalities in Fourier analysis, Ann. of math., 102, 159-182, (1975) · Zbl 0338.42017 [3] Bonami, A, Étude des coefficients de Fourier des fonctions de Lp(G), Ann. inst. Fourier Grenoble, 20, 335-402, (1970) · Zbl 0195.42501 [4] Brascamp, H.J; Lieb, E.H, Best constants in Young’s inequality, its coverse, and its generalization to more than three functions, Advances in math., 20, 151-173, (1976) · Zbl 0339.26020 [5] Carmona, R, Regularity properties of Schrödinger and Dirichlet semigroups, J. functional analysis, 33, 259-296, (1979) · Zbl 0419.60075 [6] Eckmann, J.-P, Hypercontractivity for anharmonic oscillators, J. functional analysis, 16, 388-404, (1974) · Zbl 0285.47032 [7] Faris, W.G, Product spaces and Nelson’s inequality, Helv. phys. acta, 48, 721-730, (1975) [8] Feissner, G, Hypercontractive semigroups and Sobolev’s inequality, Trans. amer. math. soc., 210, 51-62, (1975) · Zbl 0308.46034 [9] Folland, G.B, Introduction to partial differential equations, (1976), Princeton Univ. Press Princeton, N.J., · Zbl 0371.35008 [10] Glimm, J, Boson fields with nonlinear selfinteraction in two dimensions, Commun. math. phys., 8, 12-25, (1968) · Zbl 0173.29903 [11] Gross, L, Logarithmic Sobolev inequalities, Amer. J. math., 97, 1061-1083, (1975) · Zbl 0318.46049 [12] {\scS. Janson}, personal communication. [13] Nelson, E, The free markoff field, J. functional analysis, 12, 211-227, (1973) · Zbl 0273.60079 [14] Rosen, J.S, Sobolev inequalities for weight spaces and supercontractivity, Trans. amer. math. soc., 222, 367-376, (1976) · Zbl 0344.46072 [15] Rothaus, O.S, Lower bounds for eigenvalues of regular Sturm-Liouville operators and the logarithmic Sobolev inequality, Duke math. J., 45, 351-362, (1978) · Zbl 0435.47049 [16] Rudin, W, Real and complex analysis, (1966), McGraw-Hill New York · Zbl 0148.02904 [17] Simon, B, A remark on Nelson’s best hypercontractive estimates, (), 376-378 · Zbl 0441.46026 [18] Stein, E.M, Singular integrals and differentiability properties of functions, (1970), Princeton Univ. Press Princeton, N.J., · Zbl 0207.13501 [19] Strang, G, Linear algebra and its applications, (1976), Academic Press New York · Zbl 0338.15001 [20] Weissler, F.B, Logarithmic Sobolev inequalities for the heat-diffusion semigroup, Trans. amer. math. soc., 237, 255-269, (1978) · Zbl 0376.47019 [21] Weissler, F.B, Two-point inequalities, the Hermite semigroup and the Gauss-Weierstrass semigroup, J. functional analysis, 32, 102-121, (1979) · Zbl 0433.47023
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.