Estimates for integral norms of polynomials on spaces with convex measures

L. M. Arutyunyan   ; E. D. Kosov

Sbornik. Mathematics, Tome 206 (2015) no. 8, pp. 1030-1048

Résumé

We show that measurable polynomials of degree $d$ are integrable to every positive power and all their $L^p$-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 $L^1$-norm of continuous polynomials in terms of the $L^1$-norm of their restriction to any set of positive measure. Bibliography: 19 titles.

Détail

Keywords: convex measures, logarithmically convex measures, measurable polynomials.

Bibliographie

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