Spectral multiplier theorems via $H^{\infty }$ calculus and $R$-bounds

Christoph Kriegler, Lutz Weis

We prove spectral multiplier theorems for Hörmander classes ${\mathcal{H}}^{\alpha }\_p$ for 0-sectorial operators A on Banach spaces assuming a bounded $H^{\infty }(\Sigma \_\sigma )$ calculus for some $σ…