Wave-front sets of Banach function types

TL;DR

This paper extends the concept of wave-front sets to distributions associated with Fourier images of weighted translation invariant Banach function spaces, and demonstrates that pseudo-differential operators maintain their usual mapping properties within this framework.

Contribution

It introduces a new wave-front set concept for distributions linked to Fourier images of Banach function spaces and proves related mapping properties for pseudo-differential operators.

Findings

Wave-front sets are generalized to Banach function space contexts.

Pseudo-differential operators preserve mapping properties in this new setting.

Abstract

We introduce the wave-front set for distributions with respect to Fourier images of weighted translation invariant Banach function spaces. We prove that usual mapping properties for pseudo-differential operators hold in the context of such wave-front sets.