Orlicz-space Hardy and Landau-Kolmogorov inequalities for Gaussian measures

TL;DR

This paper establishes new inequalities in Orlicz spaces for Gaussian measures, extending classical Hardy and Landau-Kolmogorov inequalities to a broader functional framework.

Contribution

It introduces Orlicz-space versions of Hardy and Landau-Kolmogorov inequalities specifically for Gaussian measures, expanding the scope of these inequalities.

Findings

Derived Orlicz-space Hardy inequalities for Gaussian measures

Established Landau-Kolmogorov inequalities in the Orlicz setting

Extended classical inequalities to a more general functional space

Abstract

We prove Orlicz-space versions of Hardy and Landau-Kolmogorov inequalities for Gaussian measures on the n-dimensional Euclidean space.