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BMO spaces related to Schrödinger operators with potentials satisfying a reverse Hölder inequality

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Abstract.

We identify the dual space of the Hardy-type space related to the time independent Schrödinger operator =−Δ+V, with V a potential satisfying a reverse Hölder inequality, as a BMO-type space . We prove the boundedness in this space of the versions of some classical operators associated to (Hardy-Littlewood, semigroup and Poisson maximal functions, square function, fractional integral operator). We also get a characterization of in terms of Carlesson measures.

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References

  1. Bennet, C., DeVore, R.A., Sharpley, R.: Weak-L∞ and BMO. Ann. Math. 113, 601–611 (1981)

    Google Scholar 

  2. Dziubański, J., Zienkiewicz, J.: Hardy space H1 associated to Schrödinger operator with potential satisfying reverse Hölder inequality. Rev. Mat. Iberoam. 15(2), 279–296 (1999)

    Google Scholar 

  3. Dziubański, J., Zienkiewicz, J.: Hp spaces for Schrödinger operators. Fourier Analysis and Related Topics, Vol. 56, Banach Center Publications, 2002, pp. 45–53

  4. Dziubański, J., Zienkiewicz, J.: Hp spaces associated with Schrödinger operators with potentials from reverse Hölder classes. Colloq. Math. to appear

  5. Goldberg, D.: A local version of real Hardy spaces. Duke Math. J. 46, 27–42 (1979)

    MathSciNet  MATH  Google Scholar 

  6. Kurata, K.: An estimate on the heat kernel of magnetic Schrödinger operators and uniformly elliptic operators with non-negative potentials. J. London Math. Soc. (2) 62, 885–903 (2000)

  7. Shen, Z.: Lp estimates for Schrödinger operators with certain potentials. Ann. Inst. Fourier 45(2), 513–546 (1995)

    MATH  Google Scholar 

  8. Stein, E.: Topics in Harmonic Analysis Related to the Littlewood-Paley Theory. Princeton University Press, Princeton NJ, 1970

  9. Stein, E.: Harmonic Analysis: Real Variable Methods, Orthogonality, and Oscillatory Integrals. Princeton University Press, 1993

  10. Torchinsky, A.: Real-variable methods in harmonic analysis. Pure and Applied Mathematics, 123. Academic Press Inc., Orlando, 1986

  11. Stempak, K., Torrea, J.L.: Endpoint results for Poisson inetgrals and Riesz transforms for Hermite function expansions. Preprint

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Authors and Affiliations

  1. Institute of Mathematics, University of Wrocław, Pl. Grunwaldzki 2/4, 50-384, Wrocław, Poland

    J. Dziubański & J. Zienkiewicz

  2. Departamento de Matemáticas, Universidad Autónoma de Madrid, Ciudad Universitaria de Cantoblanco, 28049, Madrid, Spain

    G. Garrigós, T. Martínez & J. L. Torrea

Authors
  1. J. Dziubański
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  2. G. Garrigós
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  3. T. Martínez
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  4. J. L. Torrea
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  5. J. Zienkiewicz
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Corresponding author

Correspondence to J. L. Torrea.

Additional information

Mathematics Subject Classification (2000): 35J10, 42B35, 42B30

This research was partially supported by the European Commission, within the IHP Network “HARP 2002-2006”, contract number HPRN-CT-2001-00273-HARP. Second author also supported by Programa Ramón y Cajal and grant “BMF2001-0189” MCyT (Spain). The first and the fifth author supported by grants 5P03A05020 and 5P03A02821 from KBN (Poland) and by Foundation of Polish Sciences Subsidy 3/99. The third and the fourth author supported by grant MCyT BMF2002-04013-C02-02.

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Dziubański, J., Garrigós, G., Martínez, T. et al. BMO spaces related to Schrödinger operators with potentials satisfying a reverse Hölder inequality. Math. Z. 249, 329–356 (2005). https://doi.org/10.1007/s00209-004-0701-9

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  • DOI: https://doi.org/10.1007/s00209-004-0701-9

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