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 $B^s_{q,1}$-type Besov spaces on domains of $\mathbb R^n$, $n\geq 2$.
Myong-Hwan RI
,
Reinhard FARWIG
. MAXIMAL $L^1$-REGULARITY OF GENERATORS FOR BOUNDED ANALYTIC SEMIGROUPS IN BANACH SPACES[J]. Acta mathematica scientia, Series B, 2022
, 42(4)
: 1261
-1272
.
DOI: 10.1007/s10473-022-0401-8
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