Advertisement

Bilinear rough singular integral operators on Morrey spaces

  • Daniel SalimEmail author
  • Yoshihiro Sawano
  • Pebrudal Zanu
Original Research Paper
  • 11 Downloads

Abstract

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.

Keywords

Singular integral operators Bilinear operators Rough operators Morrey spaces 

Mathematics Subject Classification

42B20 42B99 

Notes

Compliance with ethical standards

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.

References

  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.MathSciNetCrossRefGoogle Scholar
  2. 2.
    Grafakos, L., D. He, and P. Honzík. 2018. Rough bilinear singular integrals. Advances in Mathematics 326: 54–78.MathSciNetCrossRefGoogle 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.MathSciNetCrossRefGoogle 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.MathSciNetCrossRefGoogle Scholar

Copyright information

© Forum D'Analystes, Chennai 2019

Authors and Affiliations

  1. 1.Analysis and Geometry Group, Faculty of Mathematics and Natural SciencesBandung Institute of TechnologyBandungIndonesia
  2. 2.Department of Mathematics and Information ScienceTokyo Metropolitan UniversityHachouji-cityJapan
  3. 3.Department of Mathematics Analysis and the Theory of functionsPeoples’ Friendship University of RussiaMoscowRussia

Personalised recommendations