Geodesic
On the boundedness of the mapping $f\to |f|$ in Besov spaces
Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992) no. 1, pp. 57-66.

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For $1\leq p\leq\infty$, precise conditions on the parameters are given under which the particular superposition operator $T:f\to |f|$ is a bounded map in the Besov space $B^s_{p,q}(R^1)$. The proofs rely on linear spline approximation theory.
Classification : 35B45, 41A15, 46E35, 47H30
Keywords: Nemytzki operators; Besov spaces; moduli of smoothness; linear splines 
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     title = {On the boundedness of the mapping $f\to |f|$ in {Besov} spaces},
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Oswald, P. On the boundedness of the mapping $f\to |f|$ in Besov spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992) no. 1, pp. 57-66. http://geodesic.mathdoc.fr/item/CMUC_1992__33_1_a7/