Maximal L1-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 (θ, 1)-type real interpolation of its domain and underlying Banach space has maximal L1-regularity, using a duality argument combined with the result of maximal continuous regularity. As an application, we consider maximal L1-regularity of the Dirichlet-Laplacian and the Stokes operator in inhomogeneous B sq,1 -type Besov spaces on domains of ℝn, n ≥ 2.