Sharp Lyapunov's inequality for the measurable sets with infinite measure, with generalization to the Grand Lebesgue spaces

TL;DR

This paper generalizes Lyapunov's inequality to infinite measure spaces and Grand Lebesgue spaces, providing exact constants and potential applications in analysis, probability, and statistics.

Contribution

It extends classical inequalities to new functional spaces with explicit constants, broadening their applicability.

Findings

Extended Lyapunov inequality to infinite measure spaces

Derived exact constants for the inequalities

Potential applications in analysis and probability theory

Abstract

We extend the classical Lyapunov inequality on the measurable space with infinite measure and on the so-called Grand Lebesgue spaces (GLS). We find also the exact value for correspondent constant. Possible applications: Functional Analysis (for instance, interpolation of operators), Integral Equations, Probability Theory and Statistics (tail estimations for random variables) etc.