Skip to main content

Advertisement

Log in

A note on the Fefferman–Stein inequality on Morrey spaces

  • Published:
Revista Matemática Complutense Aims and scope Submit manuscript

Abstract

In this paper, we discuss the Fefferman–Stein inequality on Morrey spaces and give a sufficient and necessary condition for which the inequality holds. Further, we give an example of weights such that the Fefferman–Stein inequality on Morrey spaces fails. We also consider the multilinear setting.

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. Adams, D.R., Xiao, J.: Nonlinear analysis on Morrey spaces and their capacities. Indiana Univ. Math. J. 53, 1629–1663 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  2. Adams, D.R., Xiao, J.: Morrey spaces in harmonic analysis. Ark. Mat. 50(2), 201–230 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  3. Chiarenza, F., Frasca, M.: Morrey spaces and Hardy–Littlewood maximal function. Rend. Mat. Appl. 7, 273–279 (1987)

    MathSciNet  MATH  Google Scholar 

  4. Duoandikoetxea, J.: Fourier Analysis, Graduate Studies in Mathematics, vol. 29. Amer. Math. Soc, Providence (2001)

    Google Scholar 

  5. Grafakos, L.: Modern Fourier analysis, 2nd edn, Graduate Texts in Mathematics, no 249. Springer, New York (2008)

    Google Scholar 

  6. Iida, T., Sato, E., Sawano, Y., Tanaka, H.: Weighted norm inequalities for multilinear fractional operators on Morrey spaces. Studia Math. 205, 139–170 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  7. Iida, T., Sato, E., Sawano, Y., Tanaka, H.: Sharp bounds for multilinear fractional integral operators on Morrey type spaces. Positivity 16(2), 339–358 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  8. 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, 1222–1264 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  9. Lu, S., Ding, Y., Yan, D.: Singular Integrals and Related Topics. World Scientific Publishing, Singapore (2007)

    Book  MATH  Google Scholar 

  10. Nakamura, S.: Generalized weighted Morrey spaces and classical operators. Math. Nachr., 1–28 (2016). doi:10.1002/mana.201500260

  11. Nakamura. S., Sawano. Y.: The singular integral operator and its commutator on weighted Morrey spaces. arXiv:1606.00971

  12. Sawano, Y., Sugano, S., Tanaka, H.: Orlicz–Morrey spaces and fractional operators. Potential Anal. 36, 517–556 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  13. Tanaka, H.: Two-weight norm inequalities on Morrey spaces. Annales Academia Scientarum Fennicae Math. 40, 773–791 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  14. Tanaka, H.: Private communication

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Shohei Nakamura.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Iida, T., Nakamura, S. A note on the Fefferman–Stein inequality on Morrey spaces. Rev Mat Complut 30, 525–545 (2017). https://doi.org/10.1007/s13163-016-0217-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13163-016-0217-y

Keywords

Mathematics Subject Classification

Navigation