Grand Lebesgue Spaces norm estimates for multivariate functional operations

TL;DR

This paper develops estimates for moments and tail behaviors of multivariate functional operations, which may be nonlinear, providing insights into their probabilistic properties.

Contribution

It introduces new methods for deriving moment and tail estimates for complex multivariate functional operations, including nonlinear cases.

Findings

Derived moment estimates for multivariate functional operations.

Established exponential tail bounds for these operations.

Proved the near-exactness of the estimates up to multiplicative constants.

Abstract

We intend to derive the moment and exponential tail estimates for the so-called bivariate or more generally multivariate functional operations, not necessary to be linear or even multilinear. We will show also the strong or at last weak (i.e. up to multiplicative constant) exactness of obtained estimates.