Hypercontractivity: A Bibliographic Review - Mathematics ...

380 E. Davies et al
References
[I] R . A. Adams, General logarithmic Sobolev inequalities and Orlicz imbeddings. J. Funct.
[2)
An al. II (1979 ), 292-303.
_______ and F. H. Clarke, Gross's logarithmic Sobolev in equality: a simple proof,
Amer. J. Math. ill (1979 ), 1265-1270.
[3] D. G. A ronson, Non-negative solutions of linear parabolic equations, Ann. Sci. ;\orm. Sup.
Pi,. (3) 22 (1968), 607-694 .
[4] Joel Avrim, Perturba tion of Logarithmic Sobolev generators by electric and m agnetil:
potent ials, Berkeley Thesis 1982.
[5) D. Bakry, Une remarque ,ur les dirr"'on' hyperoo",a",,,e,, P repr,nt Nov. 1987,3 pp.
[6J D. Bakry and M. Emery, Hypercontractivite de semi-groupes de diffus ion, Compte-Re ndus
[7)
299 (1984), 775-778.
_ _ _ _____ • Diffusions hypercontractives, pp. 177-207 in Sem . de P robabilites X IX.
Lecture Notes in Mathematics #1123, eds. J . Azema a nd M. Yor, Springe r' Verlag,
New York, 1985.
[8] D. Bakry and P. A. Meyer, Sur les inequalities de Sobolev logarithmique I &. II Preprints,
Vniv. de Strasbourg 1980/81.
(9] W . Beckner. Inequalities in Fourier Analysis on R n , P roc. Nat. Acad. Sci. U.S .A . 72
(1975),638-641.
[10] _______ _ , Inequalities in Fourier A nalysis, Ann. of Math . 102 ( 1975), 159·1$2.
Ill) ________ , S. Janson and D. Jerison, Convolution inequalities on the circle,
Conference on ha r monic analysis in honor of Anton i Zygm u nd , \Vadsworth,
Belmont 1983. vol. 1, 32·43.
[12J Iwo Bialynicki.Birula a nd J erzy Mycielski, Uncertainty relations for information ent·rapy in