Mapping properties for operator-valued pseudodifferential operators on toroidal Besov spaces
Analysis of PDEs
2020-08-20 v1
Abstract
In this paper, we consider pseudodifferential operators on the torus with operator-valued symbols and prove continuity properties on vector-valued toroidal Besov spaces, without assumptions on the underlying Banach spaces. The symbols are of limited smoothness with respect to and satisfy a finite number of estimates on the discrete derivatives. The proof of the main result is based on a description of the operator as a convolution operator with a kernel representation which is related to the dyadic decomposition appearing in the definition of the Besov space.
Cite
@article{arxiv.1706.07327,
title = {Mapping properties for operator-valued pseudodifferential operators on toroidal Besov spaces},
author = {Bienvenido Barraza Martínez and Robert Denk and Jairo Hernández Monzón and Max Nendel},
journal= {arXiv preprint arXiv:1706.07327},
year = {2020}
}