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