Skip to main content
SpringerLink
Log in

Sharp bounds for multilinear fractional integral operators on Morrey type spaces

  • Published:
Positivity Aims and scope Submit manuscript

Abstract

A multi-Morrey norm which is strictly smaller than m-fold product of the Morrey norms is introduced and the boundedness property of the Adams type for multilinear fractional integral operators is obtained. The optimality of the results is also discussed.

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

References

  1. Adams D.R.: A note on Riesz potentials. Duke Math. J. 42, 765–778 (1975)

    Article  MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  4. Kenig C.E., Stein E.M.: Multilinear estimates and fractional integration. Math. Res. Lett. 6, 1–15 (1999)

    MathSciNet  MATH  Google Scholar 

  5. Lerner A., 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 

  6. Moen K.: Weighted inequalities for multilinear fractional integral operators. Collect. Math. 60, 213–238 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  7. Olsen P.: Fractional integration, Morrey spaces and Schrödinger equation. Commun. Partial Differ. Equ. 20, 2005–2055 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  8. Pérez C.: Two weighted inequalities for potential and fractional type maximal operators. Indiana Univ. Math. J. 43, 663–683 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  9. Rao M., Ren Z.: Theory of Orlicz Spaces. Dekker, New York (1991)

    MATH  Google Scholar 

  10. Iida T., Sato E., Sawano Y., Tanaka H.: Multilinear fractional integrals on Morrey spaces. Acta Math. Sin. (to appear)

  11. Sawano Y., Sugano S., Tanaka H.: Orlicz-Morrey spaces and fractional operators. Potential Anal. (to appear)

  12. Shi Y., Tao X.: Multilinear Riesz potential operators on Herz-type spaces and generalized Morrey spaces. Hokkaido Math. J. 38(4), 635–662 (2009)

    MathSciNet  MATH  Google Scholar 

  13. Tang L.: Endpoint estimates for multilinear fractional integrals. J. Aust. Math. Soc. 84, 419–429 (2008)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, Faculty of Science, Yamagata University, Yamagata, 990-8560, Japan

    Takeshi Iida & Enji Sato

  2. Department of Mathematics, Kyoto University, Kyoto, 606-8502, Japan

    Yoshihiro Sawano

  3. Graduate School of Mathematical Sciences, The University of Tokyo, Tokyo, 153-8914, Japan

    Hitoshi Tanaka

Authors
  1. Takeshi Iida
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Enji Sato
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yoshihiro Sawano
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Hitoshi Tanaka
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yoshihiro Sawano.

Additional information

Y. Sawano is supported by Grant-in-Aid for Young Scientists (B) (No. 21740104) Japan Society for the Promotion of Science. H. Tanaka is supported by the Global COE program at Graduate School of Mathematical Sciences, the University of Tokyo, and was supported by Fūjyukai foundation.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Iida, T., Sato, E., Sawano, Y. et al. Sharp bounds for multilinear fractional integral operators on Morrey type spaces. Positivity 16, 339–358 (2012). https://doi.org/10.1007/s11117-011-0129-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11117-011-0129-5

Keywords

Mathematics Subject Classification (2000)

Search

Navigation