Functional calculus on real interpolation spaces for generators of $C_0$-groups

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 $H_1^{\infty }$-calculus on real interpolation spaces. Additional results are derived from this.

Final version published in Mathematische Nachrichten, with some minor changes

References in corpus (1)

• Functional calculus for semigroup generators via transference

Cited by in corpus (3)

• Fourier multiplier theorems on Besov spaces under type and cotype conditions
• Operator-valued $(L^p,L^q)$ Fourier multipliers and stability theory for evolution equations
• Functional calculus for $C_0$-groups using (co)type