Real interpoaltion of Sobolev spaces associated to a weight

Nadine Badr

Real interpoaltion of Sobolev spaces associated to a weight

Functional Analysis 2008-04-12 v2 Metric Geometry

Authors: Nadine Badr

Abstract

We study the interpolation property of Sobolev spaces of order 1 denoted by $W^{1}_{p,V}$ , arising from Schr\"{o}dinger operators with positive potential. We show that for $1\leq p_1<p<p_2<q_{0}$ with $p>s_0$ , $W^{1}_{p,V}$ is a real interpolation space between $W_{p_1,V}^{1}$ and $W_{p_2,V}^{1}$ on some classes of manifolds and Lie groups. The constants $s_{0}, q_{0}$ depend on our hypotheses.

Keywords

Sobolev spaces real interpolation Schrödinger operators positive potential manifolds Lie groups

Cite

@article{arxiv.0705.2268,
  title  = {Real interpoaltion of Sobolev spaces associated to a weight},
  author = {Nadine Badr},
  journal= {arXiv preprint arXiv:0705.2268},
  year   = {2008}
}

Comments

25 pages

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