Skip to main content
SpringerLink
Log in

Harmonic analysis operators related to symmetrized Jacobi expansions for all admissible parameters

  • Published:
Acta Mathematica Hungarica Aims and scope Submit manuscript

Abstract

This is an ultimate completion of our earlier paper [3] where mapping properties of several fundamental harmonic analysis operators in the setting of symmetrized Jacobi trigonometric expansions were investigated under certain restrictions on the underlying parameters of type. In the present article we take advantage of very recent results due to Nowak, Sjögren and Szarek to fully release those restrictions, and also to provide shorter and more transparent proofs of the previous restricted results. Moreover, we also study mapping properties of analogous operators in the parallel context of symmetrized Jacobi function expansions. Furthermore, as a consequence of our main results we conclude some new results related to the classical non-symmetrized Jacobi polynomial and function expansions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. V. Almeida, J. J. Betancor, A. J. Castro, A. Sanabria and R. Scotto, Variable exponent Sobolev spaces associated with Jacobi expansions, preprint, 2014, arXiv:1410.3642.

  2. Castro A.J., Nowak A., Szarek T.Z.: Riesz–Jacobi transforms as principal value integrals. J.Fourier Anal. Appl., 22, 493–541 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  3. Langowski B.: Harmonic analysis operators related to symmetrized Jacobi expansions. Acta Math. Hungar., 140, 248–292 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  4. Langowski B.: Sobolev spaces associated with Jacobi expansions. J. Math. Anal. Appl., 420, 1533–1551 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  5. Langowski B.: On potential spaces related to Jacobi expansions. J. Math. Anal. Appl., 432, 374–397 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  6. B. Langowski, Potential and Sobolev spaces related to symmetrized Jacobi expansions, Symmetry, Integrability and Geometry: Methods and Applications, SIGMA, 11 (2015), 073, 17 pages.

  7. Nowak A., Roncal L.: Potential operators associated with Jacobi and Fourier-Bessel expansions. J. Math. Anal. Appl., 422, 148–184 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  8. Nowak A., Sjögren P.: Calderón–Zygmund operators related to Jacobi expansions. J. Fourier Anal. Appl., 18, 717–749 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  9. Nowak A., Sjögren P.: Sharp estimates of the Jacobi heat kernel. Studia Math., 218, 219–244 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  10. Nowak A., Sjögren P., Szarek T.Z.: Analysis related to all admissible type parameters in the Jacobi setting. Constr. Approx., 41, 185–218 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  11. Nowak A., Stempak K.: L 2-theory of Riesz transforms for orthogonal expansions. J. Fourier Anal. Appl., 12, 675–711 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  12. Nowak A., Stempak K.: A symmetrized conjugacy scheme for orthogonal expansions. Proc. Royal Soc. Edinburgh Sect. A, 143, 427–443 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  13. Stempak K.: Jacobi conjugate expansions. Studia Sci. Math. Hungar., 44, 117–130 (2007)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Pure and Applied Mathematics, Wrocław University of Science and Technology, Wyb.Wyspiańskiego 27, 50-370, Wrocław, Poland

    B. Langowski

Authors
  1. B. Langowski
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to B. Langowski.

Additional information

Research supported by the National Science Centre of Poland, project no. 2013/09/N/ST1/04120.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Langowski, B. Harmonic analysis operators related to symmetrized Jacobi expansions for all admissible parameters. Acta Math. Hungar. 150, 49–82 (2016). https://doi.org/10.1007/s10474-016-0652-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10474-016-0652-8

Key words and phrases

Mathematics Subject Classification

Search

Navigation