Some approximation properties in fractional Musielak-Sobolev spaces

TL;DR

This paper investigates approximation properties in fractional Musielak-Sobolev spaces, extending known results from fractional Sobolev spaces using convolution and cutoff techniques.

Contribution

It establishes density results of smooth, compactly supported functions in fractional Musielak-Sobolev spaces, generalizing prior fractional Sobolev space findings.

Findings

Density of smooth functions in fractional Musielak-Sobolev spaces

Extension of fractional Sobolev space results to Musielak-Sobolev spaces

Use of convolution and cutoff techniques for proofs

Abstract

In this article, we show some density properties of smooth and compactly supported functions in fractional Musielak-Sobolev spaces essentially extending the results of Fiscella, Servadei, and Valdinoci obtained in the fractional Sobolev setting. The proofs of these properties are mainly based on a basic technique of convolution, joined with a cutoff, with some care needed in order not to exceed the original support.