Boundedness Properties of the Mapping $f \mapsto |f|^\mu, \: 0 < \mu < 1$ in the Framework of Besov Spaces

Preprint series: 99-17, Analysis

MSC:
46E35 Sobolev spaces and other spaces of smooth'' functions, embedding theorems, trace theorems
41A15 Spline approximation
35B45 A priori estimates

Abstract: Let $0 < \mu < 1$. For $1 \le p \le \infty$ precise conditions on the parameters are given such that the following inequality
$\| \, |f|^\mu \, | B^{s\mu}_{{p}/{\mu}, q/\mu}\| \le c \, \| \, f \, |B^s_{p,q} \|^\mu\, ,$
holds for all $f \in B^s_{p,q}$.