On the action of pseudo-differential operators on Gevrey spaces

2017/09/08 by Morisse, Baptiste
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1709.02591

Abstract

In this paper we study the action of pseudo-differential operators acting on Gevrey spaces. We introduce classes of classical symbols with spatial Gevrey regularity. As the spatial Gevrey regularity of a symbol p(⋅,ξ) may depend on the frequency ξ, the action of the associated pseudo-differential operator op(p) may induce a loss of regularity. The proof is based on a para-product decomposition.

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