Real interpoaltion of Sobolev spaces associated to a weight

Abstract

We study the interpolation property of Sobolev spaces of order 1 denoted by $W_{p,V}^1$, arising from Schrödinger operators with positive potential. We show that for $1\le p_1<p<p_2<q_0$ with $p>s_0$, $W_{p,V}^1$ 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.

25 pages

References in corpus (1)

• Maximal inequalities and Riesz transform estimates on $L^p$ spaces for Schrödinger operators with nonnegative potentials

Cited by in corpus (2)

• $L^p$ Boundedness of Riesz transform related to Schrödinger operators on a manifold
• On the Calderón-Zygmund lemma for Sobolev functions