Skip to main content
SpringerLink
Log in

Hölder estimates for pseudo-differential operators on \(\mathbb {T}^{1}\)

  • Published:
Journal of Pseudo-Differential Operators and Applications Aims and scope Submit manuscript

Abstract

In this work we provide Hölder estimates for one dimensional pseudo-differential operators defined on the Torus. A priori estimates for toroidal pseudo-differential problems also are considered.

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.

Similar content being viewed by others

References

  1. Brézis, H.: Analyse fonctionnelle : théorie et applications. Éditions Dunod, Paris (1999)

    Google Scholar 

  2. Beals, R.: \(L^p\) and Hölder estimates for pseudo-differential operators: sufficient conditions. Annales de l’institut Fourier. 29(3), 239–260 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  3. Cardona, D.: Estimativos \(L^2\) para una clase de operadores pseudodiferenciales definidos en el toro. Rev. Integr. Temas Mat. 31(2), 147–152 (2013)

    MATH  MathSciNet  Google Scholar 

  4. Delgado, J.: \(L^p\) bounds for pseudo-differential operators on the torus. Oper. Theory Adv. Appl. 231, 103–116 (2012)

    Google Scholar 

  5. Katznelson, Y.: An introduction to Harmonic Analysis. Cambridge University Press (2004)

  6. Molahajloo, S., Wong, M.W.: Pseudo-differential operators on \(\mathbb{S}^1\). In: Rodino, L., Wong M.W. (eds.) New developments in pseudo-differential operators. Operators Theory, Advances and Applications, vol. 189. Birkhäuser, pp. 297–306 (2008)

  7. Stein, E.: Harmonic Analysis: Real-variable Methods, Orthogonality and Oscillatory Integrals. Princeton (1993)

  8. Ruzhansky, M., Turunen, V.: Pseudo-differential Operators and Symmetries: Background Analysis and Advanced Topics. Birkhaüser-Verlag, Basel (2010)

  9. Ruzhansky, M., Turunen, V.: Quantization of pseudo-differential operators on the torus. J. Fourier Anal. Appl. 16, 943–982 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  10. Wong, M.W.: Discrete Fourier Analysis. Birkhaüser, Germany (2011)

    Book  MATH  Google Scholar 

  11. Zygmund, A.: Trigonometric series, 2nd ed. Cambridge University Press (1959)

Download references

Acknowledgments

I would like to thank the anonymous referee for his/her remarks which helped to improve the manuscript.

Author information

Authors and Affiliations

  1. Universidad de los Andes, Bogotá, Colombia

    Duván Cardona

Authors
  1. Duván Cardona
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Duván Cardona.

Additional information

This work has been partially supported by Universidad de los Andes, Department of Mathematics.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Cardona, D. Hölder estimates for pseudo-differential operators on \(\mathbb {T}^{1}\) . J. Pseudo-Differ. Oper. Appl. 5, 517–525 (2014). https://doi.org/10.1007/s11868-014-0099-z

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11868-014-0099-z

Keywords

Mathematics Subject Classification

Search

Navigation