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

Jacek Dziubański; Jacek Zienkiewicz

H^{p}

spaces associated with Schrödinger operators with potentials from reverse Hölder classes

Jacek Dziubański ; Jacek Zienkiewicz

Colloquium Mathematicae, Tome 96 (2003), p. 5-38 / Harvested from The Polish Digital Mathematics Library

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Résumé

Let A = -Δ + V be a Schrödinger operator on $ℝ^{d}$ , d ≥ 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 $H_{A}^{p}$ if the maximal function $s u p_{t > 0} | T_{t} f (x) |$ belongs to $L^{p} (ℝ^{d})$ , where ${T_{t}}_{t > 0}$ is the semigroup generated by -A. It is proved that for d/(d+1) < p ≤ 1 the space $H_{A}^{p}$ admits a special atomic decomposition.

Publié le : 2003-01-01

Zbl 1083.42015

EUDML-ID : urn:eudml:doc:284618

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     author = {Jacek Dziuba\'nski and Jacek Zienkiewicz},
     title = {$H^{p}$ spaces associated with Schr\"odinger operators with potentials from reverse H\"older classes},
     journal = {Colloquium Mathematicae},
     volume = {96},
     year = {2003},
     pages = {5-38},
     zbl = {1083.42015},
     language = {en},
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Jacek Dziubański; Jacek Zienkiewicz. $H^{p}$ spaces associated with Schrödinger operators with potentials from reverse Hölder classes. Colloquium Mathematicae, Tome 96 (2003) pp. 5-38. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm98-1-2/