Operator-valued $(L^p,L^q)$ Fourier multipliers and stability theory for evolution equations

Abstract

We give an overview of some recent results on operator-valued $(L^p,L^q)$ Fourier multipliers and stability theory for evolution equations. The aim is to provide a relatively nontechnical introduction to the underlying ideas, emphasizing the connection between the two areas. We also indicate how operator-valued $(L^p,L^q)$ Fourier multipliers can be applied to functional calculus theory.

arXiv commentExpository notes. Final version before publication

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• Improved polynomial decay for unbounded semigroups