Complex interpolation with Dirichlet boundary conditions on the half line

Journal article (2018)

Authors

N. Lindemulder Analysis - EEMCS
Martin Meyries Martin-Luther-Universität Halle-Wittenberg
M.C. Veraar Analysis - EEMCS
Research Group
Analysis (EEMCS) (TU Delft)
Copyright: © 2018 N. Lindemulder, Martin Meyries, M.C. Veraar
DOI: https://doi.org/10.1002/mana.201700204
Ap-weights UMD H∞-calculus Sobolev spaces Bessel potential spaces Complex interpolation with boundary conditions Pointwise multipliers
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Published Date

2018

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Analysis

Abstract

We prove results on complex interpolation of vector-valued Sobolev spaces over the half-line with Dirichlet boundary condition. Motivated by applications in evolution equations, the results are presented for Banach space-valued Sobolev spaces with a power weight. The proof is based on recent results on pointwise multipliers in Bessel potential spaces, for which we present a new and simpler proof as well. We apply the results to characterize the fractional domain spaces of the first derivative operator on the half line.