# Maximal and other operators in exponential Orlicz and Grand Lebesgue Spaces

## TL;DR

This paper provides precise non-asymptotic estimates for the norms of maximal and similar operators within exponential Orlicz and Grand Lebesgue Spaces, advancing the understanding of these operators in probabilistic functional analysis.

## Contribution

It introduces exact non-asymptotic bounds for nonlinear operators in exponential Orlicz and Grand Lebesgue Spaces, utilizing the theory of GLS.

## Key findings

- Exact estimates for maximal operator norms in exponential Orlicz spaces
- Non-asymptotic bounds for operators in Grand Lebesgue Spaces
- Application of GLS theory to operator norm estimation

## Abstract

We derive in this preprint the exact up to multiplicative constant non-asymptotical estimates for the norms of some non-linear in general case operators, for example, the so-called maximal functional operators, in two probabilistic rearrangement invariant norm: exponential Orlicz and Grand Lebesgue Spaces. We will use also the theory of the so-called Grand Lebesgue Spaces (GLS) of measurable functions.