A+ CATEGORY SCIENTIFIC UNIT

Hardy spaces $H^1$ for Schrödinger operators with certain potentials

Volume 164 / 2004

Jacek Dziubański, Jacek Zienkiewicz Studia Mathematica 164 (2004), 39-53 MSC: Primary 42B30, 42B25, 35J10; Secondary 47D03. DOI: 10.4064/sm164-1-3

Abstract

Let $\{ K_t\} _{t>0}$ be the semigroup of linear operators generated by a Schrödinger operator $-L={\mit \Delta } -V$ with $V\geq 0$. We say that $f$ belongs to $H_L^1$ if $\| \mathop {\rm sup}_{t>0}|K_tf(x)|\, \| _{L^1(dx)}<\infty $. We state conditions on $V$ and $K_t$ which allow us to give an atomic characterization of the space $H^1_L$.

Authors

  • Jacek DziubańskiInstitute of Mathematics
    University of Wrocław
    Pl. Grunwaldzki 2/4
    50-384 Wrocław, Poland
    e-mail
  • Jacek ZienkiewiczInstitute of Mathematics
    University of Wrocław
    Pl. Grunwaldzki 2/4
    50-384 Wrocław, Poland
    e-mail

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