Complex interpolation with Dirichlet boundary conditions on the half line
Functional Analysis
2018-02-27 v2 Analysis of PDEs
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.
Cite
@article{arxiv.1705.11054,
title = {Complex interpolation with Dirichlet boundary conditions on the half line},
author = {Nick Lindemulder and Martin Meyries and Mark Veraar},
journal= {arXiv preprint arXiv:1705.11054},
year = {2018}
}
Comments
Accepted for publication in Mathematische Nachrichten