Derivatives of L^p Eigenfunctions of Schrödinger Operators

Rice University, 6100 Main Street, Mathematics MS 136, Houston, TX 77005, USA

^∗ Corresponding author. E-mail: milivoje.lukic@rice.edu

Abstract

Assuming the negative part of the potential is uniformly locally L¹, we prove a pointwise L^p estimate on derivatives of eigenfunctions of one-dimensional Schrödinger operators. In particular, if an eigenfunction is in L^p, then so is its derivative, for 1 ≤ p ≤ ∞.