Annali di Matematica Pura ed Applicata (1923 -)

, Volume 184, Issue 3, pp 315–326

Hardy spaces H1 for Schrödinger operators with compactly supported potentials

Article

Abstract

Let L=-Δ+V be a Schrödinger operator on ℝd, d≥3, where V is a non-negative compactly supported potential that belongs to Lp for some p>d/2. Let {Kt}t>0 denote the semigroup of linear operators generated by -L. For a function f we define its H1L-norm by \(\| f\|_{H^1_L}=\| \sup_{t>0} |K_t f(x)|\|_{L^1(dx)}\). It is proved that for a properly defined weight w a function f belongs to H1L if and only if wfH1(ℝd), where H1(ℝd) is the classical real Hardy space.

Keywords

Hardy spaces atomic decomposition Schrödinger operators 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag 2004

Authors and Affiliations

  1. 1.Institute of MathematicsUniversity of WrocławWrocławPoland

Personalised recommendations