Functional calculus for generators of symmetric contraction semigroups

Abstract

We prove that every generator of a symmetric contraction semigroup on a $\sigma$-finite measure space admits, for $1<p<\infty$, a Hörmander-type holomorphic functional calculus on $L^p$ in the sector of angle ${\varphi }_p^{\ast }=arcsin|1-2/p|$. The obtained angle is optimal.