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Atomic characterization of the Hardy space  of one-dimensional Schrödinger operators with nonnegative potentials
Authors:
Wojciech Czaja and Jacek Zienkiewicz
Journal:
Proc. Amer. Math. Soc. 136 (2008), 89-94
MSC (2000):
Primary 35J10, 42B25, 42B30; Secondary 47D03
Published electronically:
October 12, 2007
MathSciNet review:
2350392
Full-text PDF Free Access
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Additional Information
Abstract: Given a Schrödinger operator  on  with nonnegative potential  , we present an atomic characterization of the associated Hardy space  .
- 1.
Jacek
Dziubański and Jacek
Zienkiewicz, Hardy spaces 𝐻¹ for Schrödinger
operators with certain potentials, Studia Math. 164
(2004), no. 1, 39–53. MR 2079769
(2005f:47097), http://dx.doi.org/10.4064/sm164-1-3
- 2.
A.
Pazy, Semigroups of linear operators and applications to partial
differential equations, Applied Mathematical Sciences, vol. 44,
Springer-Verlag, New York, 1983. MR 710486
(85g:47061)
- 3.
Elias
M. Stein, Harmonic analysis: real-variable methods, orthogonality,
and oscillatory integrals, Princeton Mathematical Series,
vol. 43, Princeton University Press, Princeton, NJ, 1993. With the
assistance of Timothy S. Murphy; Monographs in Harmonic Analysis, III. MR 1232192
(95c:42002)
- 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)
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Additional Information
Wojciech Czaja
Affiliation:
Institute of Mathematics, University of Wrocław, Pl. Grunwaldzki 2/4, 50-384, Wrocław, 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 Wrocław, Pl. Grunwaldzki 2/4, 50-384, Wrocław, Poland
Email:
zenek@math.uni.wroc.pl
DOI:
http://dx.doi.org/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
Published electronically:
October 12, 2007
Additional Notes:
The first author was supported in part by European Commission grant MEIF-2003-500685.
Communicated by:
Michael T. Lacey
Article copyright:
© Copyright 2007 American Mathematical Society
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