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

Jacek Dziubański¹ ; Jacek Zienkiewicz¹

¹ Institute of Mathematics University of Wrocław Pl. Grunwaldzki 2/4 50-384 Wrocław, Poland

Colloquium Mathematicum, Tome 98 (2003) no. 1, pp. 5-38.

Résumé

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.

Détail

DOI : 10.4064/cm98-1-2

Keywords: mit delta schr dinger operator mathbb geq where nonnegative potential satisfying reverse lder inequality exponent say element maximal function mathop sup belongs mathbb where semigroup generated a proved leq space admits special atomic decomposition