A transference principle for general groups and functional calculus on UMD spaces

Details A transference principle for general groups and functional calculus on UMD spaces A transference principle for general groups and functional calculus on UMD spaces

2008-07-24

arxiv.org/abs/0807.3906v1

Mathematics

Functional Analysis

17 pages, no figures. To be published in Mathematische Annalen

Scientific paper

We prove a transference principle for general (i.e., not necessarily bounded) strongly continuous groups on Banach spaces. If the Banach space has the UMD property, the transference principle leads to estimates for the functional calculus of the group generator. In the Hilbert space case, the results cover classical theorems of McIntosh and Boyadzhiev-de Laubenfels; in the UMD case they are analogues of classical results by Hieber and Pruess. By using functional calculus methods, consequences for sectorial operators are derived. For instance it is proved, that every generator of a cosine function on a UMD space has bounded H-infinity calculus on sectors.

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