Skip to main content
Log in

Triebel–Lizorkin–Morrey spaces associated to Hermite operators

  • Published:
Revista Matemática Complutense Aims and scope Submit manuscript

Abstract

The aim of this article is to establish molecular decomposition of homogeneous and inhomogeneous Triebel–Lizorkin–Morrey spaces associated to the Hermite operator \(\mathbb {H} \equiv -\Delta +|x|^2\) on the Euclidean space \(\mathbb {R}^n\). As applications of the molecular decomposition theory, we show the Triebel–Lizorkin–Morrey boundedness of Riesz potential, Bessel potential and spectral multipliers associated to the operator \({\mathbb {H}}\). These results generalize the corresponding results in Bui and Duong (J Fourier Anal Appl 21:405–448, 2015).

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

Access this article

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. Auscher, P., Ben Ali, B.: Maximal inequalities and Riesz transform estimates on \(L^p\) spaces for Schrödinger operators with non-negative potentials. Annales de I’Institut Fourier 57(6), 1975–2013 (2007)

    Article  Google Scholar 

  2. Bui, H.Q., Duong, X.T., Yan, L.: Calderón reproducing formulas and new Besov spaces associated with operators. Adv. Math. 229(4), 2449–2502 (2012)

    Article  MathSciNet  Google Scholar 

  3. Bui, T.A., Duong, X.T.: Besov and Triebel–Lizorkin spaces associated to Hermite operators. J. Fourier Anal. Appl. 21, 405–448 (2015)

    Article  MathSciNet  Google Scholar 

  4. Coulhon, T., Duong, X.T.: Maximal regularity and kernel bounds: observations on a theorem by Hieber and Prüss. Adv. Differ. Equ. 5(1–3), 343–368 (2000)

    MATH  Google Scholar 

  5. Frazier, M., Jawerth, B.: A discrete transform and decomposition of distribution spaces. J. Funct. Anal. 93, 34–170 (1990)

    Article  MathSciNet  Google Scholar 

  6. Fu, J., Xu, J.: Characterizations of Morrey type Besov and Triebel–Lizorkin spaces with variable exponents. J. Math. Anal. Appl. 381, 280–298 (2011)

    Article  MathSciNet  Google Scholar 

  7. Morrey, C.B.: On the solutions of quasi-linear elliptic partial differential equations. Trans. Am. Math. Soc. 43, 126–166 (1938)

    Article  MathSciNet  Google Scholar 

  8. Petrushev, P., Xu, Y.: Decomposition of spaces of distributions induced by Hermite expansion. J. Fourier Anal. Appl. 14(3), 372–414 (2008)

    Article  MathSciNet  Google Scholar 

  9. Sawano, Y., Tanaka, H.: Decompositions of Besov–Morrey spaces and Triebel–Lizorkin–Morrey spaces. Math. Z. 257(4), 871–905 (2007)

    Article  MathSciNet  Google Scholar 

  10. Sawano, Y.: Wavelet characterization of Besov–Morrey and Triebel–Lizorkin–Morrey spaces. Funct. Approx. Comment. Math. 38, 93–108 (2008)

    Article  MathSciNet  Google Scholar 

  11. Sawano, Y., Tanaka, H.: Besov–Morrey spaces and Triebel–Lizorkin–Morrey spaces for nondoubling measures. Math. Nachr. 282(12), 1788–1810 (2009)

    Article  MathSciNet  Google Scholar 

  12. Sawano, Y.: A note on Besov–Morrey spaces and Triebel–Lizorkin–Morrey spaces. Acta. Math. Sin. Engl. Ser. 25(8), 1223–1242 (2009)

    Article  MathSciNet  Google Scholar 

  13. Sawano, Y.: Besov–Morrey spaces and Triebel–Lizorkin–Morrey spaces on domains. Math. Nachr. 283(10), 1456–1487 (2010)

    Article  MathSciNet  Google Scholar 

  14. Tang, L., Xu, J.: Some properties of Morrey type Besov–Triebel spaces. Math. Nachr. 278, 904–917 (2005)

    Article  MathSciNet  Google Scholar 

  15. Wang, H.: Decomposition for Morrey type Besov–Triebel spaces. Math. Nachr. 282(5), 774–787 (2009)

    Article  MathSciNet  Google Scholar 

  16. Xu, J.: A characterization of Morrey type Besov and Triebel–Lizorkin spaces. Vietnam J. Math. 33(4), 369–379 (2005)

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

The authors are grateful to referee for his/her valuable suggestions which improved this paper.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Le Xuan Truong.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Trong, N.N., Truong, L.X., Dung, T.T. et al. Triebel–Lizorkin–Morrey spaces associated to Hermite operators. Rev Mat Complut 33, 527–555 (2020). https://doi.org/10.1007/s13163-019-00314-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13163-019-00314-1

Keywords

Mathematics Subject Classification

Navigation