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Functional calculus on real interpolation spaces for generators of $C_{0}$-groups (1409.6101v2)
Published 22 Sep 2014 in math.FA and math.OA
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.