Complex interpolation with Dirichlet boundary conditions on the half line
N. Lindemulder (TU Delft - Analysis)
Martin Meyries (Martin-Luther-Universität Halle-Wittenberg)
M.C. Veraar (TU Delft - Analysis)
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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.