Boundedness of pseudodifferential operators on realized homogeneous Besov spaces (Q1750684)

The paper deals with mapping properties \(f \mapsto a(x,D) f\) of the pseudodifferential operators \[ a(x,D) f = (2 \pi)^{-n} \int_{R^n} e^{ix\xi} a(x,\xi) \widehat{f} (\xi) \, d\xi, \quad x\in \mathbb R^n, \] in the framework of the homogeneous Besov spaces \(\dot{B}^\sigma_{p,q} (\mathbb R^n)\) with \(1\leq p,q \leq \infty\) and \[ \sigma < n/p \quad \text{or} \quad \sigma =n/p, \;q=1. \]