Revista Matemática Iberoamericana


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Volume 15, Issue 2, 1999, pp. 279–296
DOI: 10.4171/RMI/257

Published online: 1999-08-31

Hardy space $H^1$ associated to Schrödinger operator with potential satisfying reverse Hölder inequality

Jacek Dziubański[1] and Jacek Zienkiewicz[2]

(1) Uniwersytet Wrocławski, Wroclaw, Poland
(2) Uniwersytet Wrocławski, Wroclaw, Poland

Let $\lbrace T_t\rbrace_{t>0}$ be the semigroup of linear operators generated by a Schrödinger operator $–A = \Delta –V$  where $V$ is a nonnegative potential that belongs to a certain reverse Hölder class. We define a Hardy space $H^1_A$ be means of a maximal function associated with the semigroup $\lbrace T_t\rbrace_{t>0}$. Atomic and Riesz transforms characterizations of $H^1_A$ are shown.

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Dziubański Jacek, Zienkiewicz Jacek: Hardy space $H^1$ associated to Schrödinger operator with potential satisfying reverse Hölder inequality. Rev. Mat. Iberoam. 15 (1999), 279-296. doi: 10.4171/RMI/257