  We prove logarithmic Sobolev inequalities and concentration results for
convex functions and a class of product random vectors. The results are used to
derive tail and moment inequalities for chaos variables (in spirit of Talagrand
and Arcones, Gine). We also show that the same proof may be used for chaoses
generated by log-concave random variables, recovering results by Lochowski and
present an application to exponential integrability of Rademacher chaos.
