Characterization of Orlicz admissibility

TL;DR

This paper extends the characterization of admissible operators from classical L^p spaces to more general Orlicz spaces, providing new conditions involving semigroup generation and resolvent estimates.

Contribution

It introduces novel characterizations of admissibility in Orlicz spaces, generalizing existing L^p results to broader functional settings.

Findings

Operators generating strongly continuous semigroups are admissible in Orlicz spaces.

Admissibility is characterized by specific resolvent estimates.

The results unify and extend previous L^p space characterizations.

Abstract

In this note we extend two characterizations of admissible operators with respect to $\mathrm{L}^p$ to more general Orlicz spaces. The equivalent conditions are given by the property that an associated operator generates a strongly continuous semigroup and in terms of a resolvent estimate.