Maximal L¹-regularity of generators for bounded analytic semigroups in Banach spaces

2020/04/27 by Ri, Myong-Hwan, Farwig, Reinhard
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2004.12620

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^s_q,1-type Besov spaces on domains of \mathbb Rⁿ, n≥ 2.

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