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Maximal L1-Regularity of Generators for Bounded Analytic Semigroups in Banach Spaces

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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.

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Authors and Affiliations

  1. Institute of Mathematics, State Academy of Sciences, Pyongyang, Korea

    Myong-Hwan Ri

  2. Department of Mathematics, Darmstadt University of Technology, Darmstadt, Germany

    Reinhard Farwig

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  1. Myong-Hwan Ri
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  2. Reinhard Farwig
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Correspondence to Myong-Hwan Ri.

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Ri, MH., Farwig, R. Maximal L1-Regularity of Generators for Bounded Analytic Semigroups in Banach Spaces. Acta Math Sci 42, 1261–1272 (2022). https://doi.org/10.1007/s10473-022-0401-8

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  • DOI: https://doi.org/10.1007/s10473-022-0401-8

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