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arXiv · 1409.6101

Functional calculus on real interpolation spaces for generators of $C_{0}$-groups

Markus Haase·Jan Rozendaal
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Abstract

We study functional calculus properties of $C_{0}$-groups on real interpolation spaces, using transference principles. We obtain interpolation versions of the classical transference principle for bounded groups and of a recent transference principle for unbounded groups. Then we show that each group generator on a Banach space has a bounded $H^{\infty}_{1}$-calculus on real interpolation spaces. Additional results are derived from this.

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Markus Haase, Jan Rozendaal. 2016-04-21. Functional calculus on real interpolation spaces for generators of $C_{0}$-groups. https://doi.org/10.1002/mana.201400317

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