Orlicz Space Interpolation and Its Applications to Operator Convolution

TL;DR

This paper establishes interpolation results for noncommutative Orlicz spaces and applies them to derive convolution estimates for operators and functions in quantum harmonic analysis, advancing the understanding of operator convolutions.

Contribution

It introduces a strong-type interpolation theorem for noncommutative Orlicz spaces and applies it to obtain new Young-type convolution estimates in quantum harmonic analysis.

Findings

Proved a strong-type interpolation result for noncommutative Orlicz spaces.

Derived Young-type convolution estimates for Weyl pseudodifferential symbols.

Established convolution bounds for Werner's function-operator convolutions.

Abstract

We prove a strong-type interpolation result for noncommutative Orlicz spaces over semifinite von Neumann algebras. Based on this result, we obtain Young-type convolution estimates for the Weyl pseudodifferential symbols of operators in appropriate Orlicz-Schatten spaces. Equivalently, we prove convolution estimates of Young type for Werner's function-operator convolutions in quantum harmonic analysis.