Pseudo-differential operators of the ''exotic'' class \(L^ o_{1,1}\) in spaces of Besov and Triebel-Lizorkin type
We consider the Triebel-Lizorkin spaces \(F^ s_{p,q}\) and Besov spaces \(B^ s_{p,q}\) in the Euclidean n-space \(R_ n\). Special cases are the classical Besov spaces, Sobolev spaces, Hölder-Zygmund spaces etc. The aim of the paper is to prove the following: Let T be a pseudo-differential operator of class \(L^ 0_{1,1}\). If \(s>n(1/\min (p,q,1)-1)\) for \(q<\infty\) or \(s>n/p\) for \(q=\infty\), then, for all \(0<p<\infty\), \(0<q\leq\infty \), it holds that \(T: F^ s_{p,q}\to F^ s_{p,q}\) is continuous. A corresponding result with respect to \(B^ s_{p,q}\) is also proved.
scientific article; zbMATH DE number 3875980