Revista Matemática Iberoamericana


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Volume 28, Issue 4, 2012, pp. 1035–1060
DOI: 10.4171/RMI/702

Published online: 2012-10-14

On Hardy spaces associated with certain Schrödinger operators in dimension 2

Jacek Dziubański[1] and Jacek Zienkiewicz[2]

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

We study the Hardy space $H^1$ associated with the Schrödinger operator $L=-\Delta +V$ on $\mathbb R^2$, where $V\geq 0$ is a compactly supported non-zero $C^2$-potential. We prove that this space, which is originally defined by means of the maximal function associated with the semigroup generated by $-L$, admits a special atomic decomposition with atoms satisfying a~weighted cancellation condition with a weight of logarithmic growth.

Keywords: Hardy spaces, maximal functions, Schrödinger operator

Dziubański Jacek, Zienkiewicz Jacek: On Hardy spaces associated with certain Schrödinger operators in dimension 2. Rev. Mat. Iberoamericana 28 (2012), 1035-1060. doi: 10.4171/RMI/702