Some remarks on functionals with the tensorization property

• Autorzy: Wolff P.
• Języki publikacji: EN

Abstrakty

EN

We investigate the subadditivity property also known as the tensorization property of (φ-entropy functionals and their iterations. In particular we show that the only iterated φ-entropies with the tensorization property are iterated variances. This is a complement to the result due to Latala and Oleszkiewicz on characterization of the standard φ-entropies with the tensorization property.

Słowa kluczowe

EN

product measure; convex functional; entropy; non-negativity; tensorization property

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2007
• Tom: Vol. 55, no 3
• Strony: 279--291
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Wolff P.

• Institute of Mathematics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland,

Bibliografia

• [1] W. Beckner, A generalized Poincare inequality for Gaussian measures, Proc. Amer. Math. Soc. 105 (1989), 397-400
• [2] S. Boucheron, O. Bousquet, G. Lugosi and P. Massart, Moment inequalities for functions of independent random variables, Ann. Probab. 33 (2005), 514-560.
• [3] R. Latała and K. Oleszkiewicz, Between Sobolev and Poincare, in: Geometric Aspects of Functional Analysis, Lecture Notes in Math. 1745, Springer, Berlin, 2000, 147-168.
• [4] M. Ledoux, On Talagrand's deviation inequalities for product measures, ESAIM Probab. Statist. 1 (1997), 63-87.
• [5] S. Mazur und W. Orlicz, Grundlegende Eigenschaften der polynomischen Operatio- rien. Erste Mitteilung, Studia Math. 5 (1934), 50-68.
• [6] K. Oleszkiewicz, Generalization of the hypercontraction method and the Khinchin- Kahane inequalities, Master's Thesis, Warsaw Univ., 1994 (in Polish).