Kahane-Salem-Zygmund polynomial inequalities via Rademacher processes

We prove new abstract inequalities for the expectation of the supremum norm of homogeneous Bernoulli polynomials on the unit ball of a Banach space. The development of this type of estimates was stimulated by the classical Kahane-Salem-Zygmund inequality and its recent extensions. We combine ideas from stochastic processes and interpolation theory to control increments of a Rademacher process in an Orlicz space via entropy integrals. To do this we prove general estimates for entropy integrals. We discuss applications to the study of multidimensional Bohr radii and unconditionality in spaces of homogeneous polynomials on Banach spaces. We specialize our results beyond ℓp-spaces and are able to prove variants of Bayart's results in the setting of Orlicz sequence spaces.