Skip to main content
SpringerLink
Log in

Cotlar-type inequality and weighted boundedness for maximal multilinear singular integrals in Dunkl setting

  • Original Paper
  • Published:
Advances in Operator Theory Aims and scope Submit manuscript

Abstract

In this article, we establish a multilinear Cotlar-type inequality for the maximal multilinear singular integrals in Dunkl setting whose kernels possess less regularity conditions compared to the multilinear Calderón–Zygmund kernels in spaces of homogeneous type. As applications, we achieve weighted boundedness of maximal multilinear Dunkl–Calderón–Zygmund singular integrals and pointwise convergence of principal value integrals associated with multilinear Dunkl–Calderón–Zygmund kernels.

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

Data availability

Not applicable.

References

  1. Coifman, R.R., Meyer, Y.: On commutators of singular integrals and bilinear singular integrals. Trans. Am. Math. Soc. 212, 315–331 (1975)

    Article  MathSciNet  Google Scholar 

  2. Dunkl, C.F.: Differential-difference operators associated to reflection groups. Trans. Am. Math. Soc. 311(1), 167–183 (1989)

    Article  MathSciNet  Google Scholar 

  3. Duong, X.T., Gong, R., Grafakos, L., Li, J., Yan, L.: Maximal operator for multilinear singular integrals with non-smooth kernels. Ind. Univ. Math. J. 58(6), 2517–2541 (2009)

    Article  MathSciNet  Google Scholar 

  4. Grafakos, L., Liu, L., Maldonado, D., Yang, D.: Multilinear analysis on metric spaces. Diss. Math. 497, 121 (2014)

    MathSciNet  Google Scholar 

  5. Grafakos, L., Liu, L., Yang, D.: Multiple-weighted norm inequalities for maximal multilinear singular integrals with non-smooth kernels. Proc. R. Soc. Edinb. Sect. A 141(4), 755–775 (2011)

    Article  Google Scholar 

  6. Grafakos, L., Torres, R.H.: Discrete decompositions for bilinear operators and almost diagonal conditions. Trans. Am. Math. Soc. 354(3), 1153–1176 (2002)

    Article  MathSciNet  Google Scholar 

  7. Grafakos, L., Torres, R.H.: Maximal operator and weighted norm inequalities for multilinear singular integrals. Ind. Univ. Math. J. 51(5), 1261–1276 (2002)

    Article  MathSciNet  Google Scholar 

  8. Grafakos, L., Torres, R.H.: Multilinear Calderón–Zygmund theory. Adv. Math. 165(1), 124–164 (2002)

    Article  MathSciNet  Google Scholar 

  9. Lerner, A.K., Ombrosi, S., Pérez, C., Torres, R.H., Trujillo-González, R.: New maximal functions and multiple weights for the multilinear Calderón–Zygmund theory. Adv. Math. 220(4), 1222–1264 (2009)

    Article  MathSciNet  Google Scholar 

  10. Mukherjee, S., Parui, S.: Weighted bilinear multiplier theorems in Dunkl setting via singular integrals. Preprint arXiv:2311.04754 (2023)

  11. Tan, C., Han, Y., Han, Y., Lee, M.-Y., Li, J.: Singular integral operators, T1 theorem, Littlewood–Paley theory and Hardy spaces in Dunkl setting. Preprint arXiv:2204.01886 (2022)

  12. Tan, C., Han, Y., Li, J.: Maximal operator, Cotlar’s inequality and pointwise convergence for singular integral operators in Dunkl setting. J. Geom. Anal. 33(5), 164, 18 (2023)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

Suman Mukherjee is supported by research fellowship from Department of Atomic Energy (DAE), Government of India.

Author information

Authors and Affiliations

  1. School of Mathematical Sciences, National Institute of Science Education and Research, Bhubaneswar, 752050, India

    Suman Mukherjee

  2. Homi Bhabha National Institute, Training School Complex, Anushaktinagar, Mumbai, 400094, India

    Suman Mukherjee

Authors
  1. Suman Mukherjee
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Suman Mukherjee.

Additional information

Communicated by Ferenc Weisz.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mukherjee, S. Cotlar-type inequality and weighted boundedness for maximal multilinear singular integrals in Dunkl setting. Adv. Oper. Theory 9, 38 (2024). https://doi.org/10.1007/s43036-024-00338-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s43036-024-00338-5

Keywords

Mathematics Subject Classification

Search

Navigation