Bilinear rough singular integral operators on Morrey spaces


Recently Grafakos et al., have proved that the bilinear rough singular integral operators are bounded on Lebesgue spaces. Here we aim to show that these operators extend to bounded linear operators on Morrey spaces as well. Although the proof hinges on the boundedness due to Grafakos et al., the proof seems to give a general technique to prove or extend the boundedness of the operators.

This is a preview of subscription content, access via your institution.


  1. 1.

    Ding, Y., and T. Mei. 2015. Boundedness and compactness for the commutators of bilinear operators on Morrey spaces. Potential Analysis 42 (3): 717–748.

    MathSciNet  Article  Google Scholar 

  2. 2.

    Grafakos, L., D. He, and P. Honzík. 2018. Rough bilinear singular integrals. Advances in Mathematics 326: 54–78.

    MathSciNet  Article  Google Scholar 

  3. 3.

    Rosenthal, M., and H.-J. Schmeisser. 2016. The boundedness of operators in Muckenhoupt weighted Morrey spaces via extrapolation techniques and duality. Revista Matematica Complutense 29 (3): 623–657.

    MathSciNet  Article  Google Scholar 

  4. 4.

    Triebel, H. 2014. Hybrid function spaces, heat and Navier-Stokes equations. EMS tracts in mathematics. European Mathematical Society (EMS) 24: 121. Zürich.

    Google Scholar 

  5. 5.

    Zorko, C.T. 1986. Morrey space. Proceedings of the American Mathematical Society 98: 586–592.

    MathSciNet  Article  Google Scholar 

Download references

Author information



Corresponding author

Correspondence to Daniel Salim.

Ethics declarations

Conflicts of interest

The authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

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

Verify currency and authenticity via CrossMark

Cite this article

Salim, D., Sawano, Y. & Zanu, P. Bilinear rough singular integral operators on Morrey spaces. J Anal 28, 817–825 (2020).

Download citation


  • Singular integral operators
  • Bilinear operators
  • Rough operators
  • Morrey spaces

Mathematics Subject Classification

  • 42B20
  • 42B99