Estimates for Norms of Random Polynomials

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This paper contains some estimates for the 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.