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arXiv · 1706.07327

Mapping properties for operator-valued pseudodifferential operators on toroidal Besov spaces

Bienvenido Barraza Martínez·Robert Denk·Jairo Hernández Monzón·Max Nendel
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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 $x$ 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.

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Bienvenido Barraza Martínez, Robert Denk, Jairo Hernández Monzón, Max Nendel. 2017-06-22. Mapping properties for operator-valued pseudodifferential operators on toroidal Besov spaces. https://doi.org/10.1007/s11868-017-0224-x

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