A Besov class functional calculus for bounded holomorphic semigroups (Q2577500)

Sectorial operators play an important role in functional analysis. This class of operators is used to solve many class of partial differential equations. A typical example of sectorial operators is the infinitesimal generator of a holomorphic semigroup. The aim of this paper is to study holomorphic bounded \(C_0\)-semigroups. In this work, the author uses the well-known \(H^\infty\) calculus to characterize bounded holomorphic \(C_0\)-semigroups in Banach spaces. It is proved that a holomorphic semigroup is bounded if and only if it is uniformly Tadmor--Ritt. Many applications are obtained for embedding theorems.