Derivatives of L^p eigenfunctions of Schrodinger operators

Abstract

Assuming the negative part of the potential is uniformly locally $L^1$, we prove a pointwise $L^p$ estimate on derivatives of eigenfunctions of one-dimensional Schrodinger operators. In particular, if an eigenfunction is in $L^p$, then so is its derivative, for $1\le p\le \infty$.

arXiv comment7 pages