Fredholm Property of Non-Smooth Pseudodifferential Operators

TL;DR

This paper establishes conditions under which non-smooth pseudodifferential operators with Hölder continuous symbols possess the Fredholm property, using symbol smoothing techniques.

Contribution

It introduces sufficient conditions for the Fredholm property of non-smooth pseudodifferential operators with Hölder continuous symbols, advancing understanding of their analytical behavior.

Findings

Identifies sufficient conditions for Fredholm property

Uses symbol-smoothing to handle non-smooth symbols

Extends classical results to non-smooth context

Abstract

In this paper we prove sufficient conditions for the Fredholm property of a non-smooth pseudodifferential operator $P$ which symbol is in a H\"older space with respect to the spatial variable. As a main ingredient for the proof we use a suitable symbol-smoothing.