P. Oswald
On the boundedness of the mapping $f\to |f|$ in Besov spaces

Comment.Math.Univ.Carolinae 33,1 (1992) 57-66.

Abstract: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.

Keywords: Nemytzki operators, Besov spaces, moduli of smoothness, linear splines
AMS Subject Classification: 46E35, 41A15, 35B45

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