TY - JOUR
T1 - On Fractional Smoothness of Modulus of Functions
AU - Li , Dong
JO - Annals of Applied Mathematics
VL - 3
SP - 394
EP - 404
PY - 2021
DA - 2021/09
SN - 37
DO - http://doi.org/10.4208/aam.OA-2021-0006
UR - https://global-sci.org/intro/article_detail/aam/19852.html
KW - Nemytskii, nonlocal extension,  fractional Laplacian.
AB - <p style="text-align: justify;">We consider the Nemytskii operators $u\to |u|$ and $u\to u^{\pm}$ in a bounded domain $\Omega$ with $C^2$ boundary. We give elementary proofs of the boundedness in $H^s(\Omega)$ with $0\le s&lt;3/2$.</p>