Proceedings of the American Mathematical Society

Atomic characterization of the Hardy space $H^1_L(\mathbb{R})$ of one-dimensional Schrödinger operators with nonnegative potentials

Author(s): Wojciech Czaja; Jacek Zienkiewicz
Journal: Proc. Amer. Math. Soc. 136 (2008), 89-94.
MSC (2000): Primary 35J10, 42B25, 42B30; Secondary 47D03
Posted: October 12, 2007
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Abstract: Given a Schrödinger operator $L=\frac{d^2}{dx^2}-V(x)$ on $\mathbb{R}$ with nonnegative potential

, we present an atomic characterization of the associated Hardy space $H_L^1 (\mathbb{R})$ .

1.: J. Dziubanski, J. Zienkiewicz, Hardy spaces for Schrödinger operators with certain potentials, Studia Math. 164 (2004), 39-53. MR 2079769 (2005f:47097)
2.: A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, New York, NY, 1983. MR 710486 (85g:47061)
3.: E. M. Stein, Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton University Press, Princeton, NJ, 1993. MR 1232192 (95c:42002)

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 35J10, 42B25, 42B30, 47D03

Wojciech Czaja
Affiliation: Institute of Mathematics, University of Wroclaw, Pl. Grunwaldzki 2/4, 50-384, Wroclaw, Poland
Address at time of publication: Department of Mathematics, University of Maryland, College Park, Maryland 20742
Email: wojtek@math.umd.edu

Jacek Zienkiewicz
Affiliation: Institute of Mathematics, University of Wroclaw, Pl. Grunwaldzki 2/4, 50-384, Wroclaw, Poland
Email: zenek@math.uni.wroc.pl

DOI: 10.1090/S0002-9939-07-09096-X
PII: S 0002-9939(07)09096-X
Keywords: Atomic decompositions, Hardy spaces, Schr\"{o}dinger operators
Received by editor(s): August 25, 2005
Posted: October 12, 2007
Additional Notes: The first author was supported in part by European Commission grant MEIF-2003-500685.
Communicated by: Michael T. Lacey
Copyright of article: Copyright 2007, American Mathematical Society

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