Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Atomic characterization of the Hardy space $ H^1_L(\mathbb{R})$ 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

Abstract | References | Similar Articles | Additional Information

Abstract: Given a Schrödinger operator $ L=\frac{d^2}{dx^2}-V(x)$ on $ \mathbb{R}$ with nonnegative potential $ V$, we present an atomic characterization of the associated Hardy space $ H_L^1 (\mathbb{R})$.


References [Enhancements On Off] (What's this?)

  • 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, 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
  • 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

Similar Articles

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

Retrieve articles in all journals with MSC (2000): 35J10, 42B25, 42B30, 47D03


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: https://doi.org/10.1090/S0002-9939-07-09096-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