Hardy spaces associated with some Schrödinger operators

Jacek Dziubański; Jacek Zienkiewicz

Studia Mathematica (1997)

  • Volume: 126, Issue: 2, page 149-160
  • ISSN: 0039-3223

Abstract

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For a Schrödinger operator A = -Δ + V, where V is a nonnegative polynomial, we define a Hardy H A 1 space associated with A. An atomic characterization of H A 1 is shown.

How to cite

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Dziubański, Jacek, and Zienkiewicz, Jacek. "Hardy spaces associated with some Schrödinger operators." Studia Mathematica 126.2 (1997): 149-160. <http://eudml.org/doc/216448>.

@article{Dziubański1997,
abstract = {For a Schrödinger operator A = -Δ + V, where V is a nonnegative polynomial, we define a Hardy $H_A^1$ space associated with A. An atomic characterization of $H_A^1$ is shown.},
author = {Dziubański, Jacek, Zienkiewicz, Jacek},
journal = {Studia Mathematica},
keywords = {Hardy spaces; Schrödinger operator; atomic decomposition},
language = {eng},
number = {2},
pages = {149-160},
title = {Hardy spaces associated with some Schrödinger operators},
url = {http://eudml.org/doc/216448},
volume = {126},
year = {1997},
}

TY - JOUR
AU - Dziubański, Jacek
AU - Zienkiewicz, Jacek
TI - Hardy spaces associated with some Schrödinger operators
JO - Studia Mathematica
PY - 1997
VL - 126
IS - 2
SP - 149
EP - 160
AB - For a Schrödinger operator A = -Δ + V, where V is a nonnegative polynomial, we define a Hardy $H_A^1$ space associated with A. An atomic characterization of $H_A^1$ is shown.
LA - eng
KW - Hardy spaces; Schrödinger operator; atomic decomposition
UR - http://eudml.org/doc/216448
ER -

References

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  1. [D] J. Dziubański, A note on Schrödinger operators with polynomial potentials, preprint. Zbl0919.43005
  2. [DHJ] J. Dziubański, A. Hulanicki, and J. W. Jenkins, A nilpotent Lie algebra and eigenvalue estimates, Colloq. Math. 68 (1995), 7-16. Zbl0837.43012
  3. [Fe] C. Fefferman, The uncertainty principle, Bull. Amer. Math. Soc. 9 (1983), 129-206. Zbl0526.35080
  4. [FeS] C. Fefferman and E. Stein, H p spaces of several variables, Acta Math. 129 (1972), 137-193. Zbl0257.46078
  5. [FS] G. Folland and E. Stein, Hardy Spaces on Homogeneous Groups, Princeton Univ. Press, Princeton, 1982. Zbl0508.42025
  6. [G] P. Głowacki, Stable semi-groups of measures as commutative approximate identities on nongraded homogeneous groups, Invent. Math. 83 (1986), 557-582. Zbl0595.43006
  7. [Go] D. Goldberg, A local version of real Hardy spaces, Duke Math. J. 46 (1979), 27-42. 
  8. [He] W. Hebisch, On operators satisfying Rockland condition, preprint, Univ. of Wrocław. 
  9. [HN] B. Helffer et J. Nourrigat, Une inégalité L 2 , preprint. 
  10. [S1] E. M. Stein, Topics in Harmonic Analysis Related to the Littlewood-Paley Theory, Princeton Univ. Press, Princeton, 1970. Zbl0193.10502
  11. [S2] E. M. Stein, Harmonic Analysis, Princeton Univ. Press, Princeton, 1993. 
  12. [Z] J. Zhong, Harmonic analysis for some Schrödinger type operators, Ph.D. thesis, Princeton Univ., 1993. 

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