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Hypercontractivity of simple random variables

Paweł Wolff — 2007

Studia Mathematica

The optimal hypercontractivity constant for a natural operator semigroup acting on a discrete finite probability space is established up to a universal factor. The two-point spaces are proved to be the extremal case. The constants obtained are also optimal in the related moment inequalities for sums of independent random variables.

Some Remarks on Functionals with the Tensorization Property

Paweł Wolff — 2007

Bulletin of the Polish Academy of Sciences. Mathematics

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 Latała and Oleszkiewicz on characterization of the standard φ-entropies with the tensorization property.

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