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| On Fractional Smoothness of Modulus of Functions |
| Dong Li |
| (SUSTech International Center for Mathematics and Department
of Mathematics, Southern University of Science and Technology,
Shenzhen, Guangdong 518055, China) |
| DOI： |
| Abstract: |
| 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 $0\le s<3/2$. |
| Key words: Nemytskii, nonlocal extension, fractional Laplacian. |