Weighted L^p estimates for powers of selfadjoint operators

Abstract

We prove $L^p$ and weighted $L^p$ estimates for bounded functions of a selfadjoint operator satisfying both a pointwise gaussian estimate for its heat kernel and a finite speed of propagation property. As an application, we obtain weighted estimates for fractiional powers of an electromagnetic Schrödinger operator with singular coefficienta. The proofs are based on a modification of techniques due to Hebisch and Auscher and Martell. EDIT: second version, November 2010, a few inaccuracies have been corrected.

We added references and improved substantially some results

References in corpus (1)

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