2002/10/22 by Pavel Grigoriev
Mathematics · #math.PR #math.CA #msc:60G99 #msc:60G70 #msc:26D15
published as East Journal of Approximation 2001 v. 7 no. 4 pp.445--469 · Almost the same text was published in East J. Approximation 2001 v. 7 no. 4 pp. 445--469
arxiv created 2002/10/22 · arxiv updated 2009/11/30
This paper contains some estimates for the \it integral-uniform norm and the uniform norm of a wide class of random polynomials. The family of integral-uniform norms introduced by Kasin and Tzafriri is a natural generalization of the maximum norm taken over a net. We prove some properties of the integral-uniform norms. The given application of the established estimates demonstrates that the integral-uniform norms may be useful whenever one is interested in the properties of a function distribution. Key words: integral-uniform norm; random polynomials with respect to a general function system; trigonometric polynomials with random coefficients.