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Odd BMO\({(\mathbb{R})}\) Functions and Carleson Measures in the Bessel Setting

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Abstract

In this paper, we characterize the odd functions in BMO\({(\mathbb{R})}\) by using Carleson measures associated with Poisson and heat semigroups for Bessel operators.

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References

  1. Andersen K.F., Muckenhoupt B.: Weighted weak type Hardy inequalities with applications to Hilbert transforms and maximal functions. Stud. Math. 72(1), 9–26 (1982)

    MATH  MathSciNet  Google Scholar 

  2. Auscher P., Russ E., Tchamitchian P.: Hardy Sobolev spaces on strongly Lipschitz domains of \({\mathbb{R}^n}\). J. Funct. Anal. 218(1), 54–109 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  3. Betancor J.J., Fariña J.C., Martínez T., Torrea J.L.: Riesz transform and g-functions associated with Bessel operators and their appropriate Banach spaces. Israel J. Math. 157, 259–282 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  4. Chang D.-C., Krantz S.G., Stein E.M.: H p theory on a smooth domain in \({\mathbb{R}^{N}}\) and elliptic boundary value problems. J. Funct. Anal. 114(2), 286–347 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  5. Deng D., Duong X.T., Sikora A., Yan L.: Comparison of the classical BMO with the BMO spaces associated with operators and applications. Rev. Mat. Iberoam. 24(1), 267–296 (2008)

    MATH  MathSciNet  Google Scholar 

  6. Fridli S.: Hardy spaces generated by an integrability condition. J. Approx. Theory 113(1), 91–109 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  7. Haimo D.T.: Integral equations associated with Hankel convolutions. Trans. Am. Math. Soc. 116, 330–375 (1965)

    Article  MATH  MathSciNet  Google Scholar 

  8. Hirschman I.I. Jr: Variation diminishing Hankel transforms. J. Anal. Math. 8, 307–336 (1960)

    Article  MathSciNet  Google Scholar 

  9. Lebedev N.N.: Special functions and their applications. Dover, New York (1972)

    MATH  Google Scholar 

  10. Muckenhoupt B., Stein E.M.: Classical expansions and their relation to conjugate harmonic functions. Trans. Am. Math. Soc. 118, 17–92 (1965)

    Article  MATH  MathSciNet  Google Scholar 

  11. Stein, E.M.: Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals. In: Princeton Mathematical Series, vol. 43. Princeton University Press, Princeton (1993)

  12. Stempak, K.: The Littlewood–Paley theory for the Fourier-Bessel transfom. Preprint n. 45, Math. Inst. Univ. Wroclaw, Poland (1985)

  13. Titchmarsh E.C.: Hankel transforms. Proc. Camb. Phil. Soc. 21, 463–473 (1923)

    MATH  Google Scholar 

  14. Watson G.N.: A treatise on the theory of Bessel functions. Cambridge Mathematical Library. Cambridge University Press, Cambridge (1995)

    Google Scholar 

  15. Weinstein A.: Discontinuous integrals and generalized potential theory. Trans. Am. Math. Soc. 63, 342–354 (1948)

    Article  MATH  Google Scholar 

  16. Zemanian A.H.: Generalized integral transformations. Dover, New York (1987)

    MATH  Google Scholar 

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Correspondence to L. Rodríguez-Mesa.

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This paper is partially supported by MTM2007/65609.

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Betancor, J.J., Ruiz, A.C., Fariña, J.C. et al. Odd BMO\({(\mathbb{R})}\) Functions and Carleson Measures in the Bessel Setting. Integr. Equ. Oper. Theory 66, 463–494 (2010). https://doi.org/10.1007/s00020-010-1757-z

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  • DOI: https://doi.org/10.1007/s00020-010-1757-z

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