Composition operators on Besov spaces in the limiting case $s=1+1/p$
Volume 241 / 2018
Studia Mathematica 241 (2018), 1-15
MSC: Primary 46E35; Secondary 47H30.
DOI: 10.4064/sm8136-4-2017
Published online: 6 November 2017
Abstract
For $f: \mathbb{R} \to\mathbb{R}$ such that $f(0)=0$ and $f’\in L_{\infty}(\mathbb{R}) \cap \dot{B}^{1/p}_{p,\infty}(\mathbb{R})$, we show that the composition operator $T_f: g\mapsto f\circ g$ takes $ B^{1+1/p}_{p,1}(\mathbb{R}^n)$ into $B^{1+1/p}_{p,\infty}(\mathbb{R}^n)$. Hence we deduce the boundedness of $T_f$ on Besov spaces $B^{s}_{p,q}(\mathbb{R}^n)$ for $0
