$H^{p}$ spaces associated with Schrödinger operators with potentials from reverse Hölder classes

Tom 98 / 2003

Jacek Dziubański, Jacek Zienkiewicz Colloquium Mathematicum 98(2003), 5-38 MSC: Primary 42B30, 42B25, 35J10; Secondary 47D03. DOI: 10.4064/cm98-1-2 Opublikowany online: 1 January 1970

Streszczenie

Let $A=-{\mit \Delta } +V$ be a Schrödinger operator on ${{\mathbb R}}^d$, $d\geq 3$, where $V$ is a nonnegative potential satisfying the reverse Hölder inequality with an exponent $q>d/2$. We say that $f$ is an element of $H^p_A$ if the maximal function $\mathop {\rm sup}_{t>0} |T_tf(x)|$ belongs to $L^p({{\mathbb R}}^d)$, where $\{ T_t\} _{t>0}$ is the semigroup generated by $-A$. It is proved that for $d/(d+1)< p\leq 1$ the space $H^p_A$ admits a special atomic decomposition.

Autorzy

  • 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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