Moment and exponential tail estimations for norms of random variables and random operators in mixed (anisotropic) Lebesgue-Riesz spaces

TL;DR

This paper investigates the properties of random variables in mixed Lebesgue-Riesz spaces, providing conditions for their inclusion, tail estimates, especially exponential decay, and applications to random integral operators.

Contribution

It introduces new sufficient conditions for random variables to belong to mixed Lebesgue-Riesz spaces and derives tail estimates, including exponential decay, for their norms.

Findings

Established conditions for random variables in mixed Lebesgue-Riesz spaces.

Derived exponential tail estimates for norms of these variables.

Applied results to estimate norms of random integral operators.

Abstract

We study the random variables (r.v.) with values in the so-called mixed (anisotropic) Lebesgue-Riesz spaces: formulate the sufficient conditions for belonging of the r.v. to these spaces, estimate the tail of norms distribution, especially deduce the exponential decreasing tails of them, etc. We obtain as a consequence the estimations of the norms of random integral operators acting between these spaces.