MAXIMAL $L^1$-REGULARITY OF GENERATORS FOR BOUNDED ANALYTIC SEMIGROUPS IN BANACH SPACES

doi:10.1007/s10473-022-0401-8

Abstract

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 $B^s_{q,1}$-type Besov spaces on domains of $\mathbb R^n$, $n\geq 2$.

Key words: Maximal $L^1$-regularity, sectorial operator, Stokes operator

CLC Number:

35K90

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.

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