Estimates for integral norms of polynomials on spaces with convex measures

Abstract

We show that measurable polynomials of degree are integrable to every positive power and all their -norms are equivalent. We also prove a zero-one law for level sets of measurable polynomials and for sets of convergence of measurable polynomials of fixed degree on spaces with convex measures. We obtain an estimate for the -norm of continuous polynomials in terms of the -norm of their restriction to any set of positive measure. Bibliography: 19 titles.