# A note on truncations in fractional Sobolev spaces

## TL;DR

This paper investigates the behavior of specific nonlinear operators, namely the absolute value and positive/negative part functions, within fractional Sobolev spaces for smoothness levels greater than one.

## Contribution

It provides new insights into the properties and effects of truncation operators in fractional Sobolev spaces, extending understanding beyond integer-order cases.

## Key findings

- Analysis of Nemytskii operators in fractional Sobolev spaces for s>1
- Characterization of operator boundedness and continuity
- Implications for nonlinear analysis in fractional spaces

## Abstract

We study the Nemytskii operators $u\mapsto |u|$ and $u\mapsto u^{\pm}$ in fractional Sobolev spaces $H^s(\mathbb R^n)$, $s>1$.