Holomorphic calculus on $L^p(\ell^q)$ I: optimal angles

Abstract

Let $L$ generate a symmetric contraction semigroup. We prove a holomorphic Hörmander calculus on $L^p(X;\ell^q)$ at the optimal angle $\max\{\arcsin|1-2/p|,\arcsin|1-2/q|\}$, with boundary Sobolev order $s>3$.