Maximal $L^1$-regularity of generators for bounded analytic semigroups in Banach spaces

Abstract

In this paper, we prove that the generator of any bounded analytic semigroup in $(\theta ,1)$-type real interpolation of its domain and underlying Banach space has maximal $L^1$-regularity, using a duality argument combined with the result of maximal continuous regularity. As an application, we consider maximal $L^1$-regularity of the Dirichlet-Laplacian and the Stokes operator in inhomogeneous $B_{q,1}^s$-type Besov spaces on domains of ${\mathbb{R}}^n$, $n\ge 2$.