This chapter is based on the presentation “Generalized bilinear CalderónZygmund operators and applications” delivered by the author during the 2008 February Fourier Talks at the Norbert Wiener Center for Harmonic Analysis and Applications, Department of Mathematics, University of Maryland, College Park, on February 21st. In turn, that presentation was based on material from the article “Weighte...

A comprehensive analysis of Sobolev-type inequalities for the Ornstein-Uhlenbeck operator in Gauss space is offered. unified approach proposed, providing one with criteria their validity class rearrangement-invariant function norms. Optimal target and domain norms relevant are characterized via a reduction principle to one-dimensional Calderón type integral patterned on Gaussian isoperimetric f...