, Volume 16, Issue 2, pp 339–358 | Cite as

Sharp bounds for multilinear fractional integral operators on Morrey type spaces

  • Takeshi Iida
  • Enji Sato
  • Yoshihiro Sawano
  • Hitoshi Tanaka


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.


Morrey space Multilinear fractional integral operator Multilinear fractional maximal operator Multilinear Calderón-Zygmund operator Adams’ inequality 

Mathematics Subject Classification (2000)

Primary 42B35 Secondary 42B25 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Adams D.R.: A note on Riesz potentials. Duke Math. J. 42, 765–778 (1975)MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    Chiarenza F., Frasca M.: Morrey spaces and Hardy-Littlewood maximal function. Rend. Math. Appl. 7, 273–279 (1987)MathSciNetMATHGoogle Scholar
  3. 3.
    Grafakos L., Torres R.H.: Multilinear Calderón-Zygmund theory. Adv. Math. 165, 124–164 (2002)MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    Kenig C.E., Stein E.M.: Multilinear estimates and fractional integration. Math. Res. Lett. 6, 1–15 (1999)MathSciNetMATHGoogle Scholar
  5. 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)MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Moen K.: Weighted inequalities for multilinear fractional integral operators. Collect. Math. 60, 213–238 (2009)MathSciNetMATHCrossRefGoogle Scholar
  7. 7.
    Olsen P.: Fractional integration, Morrey spaces and Schrödinger equation. Commun. Partial Differ. Equ. 20, 2005–2055 (1995)MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    Pérez C.: Two weighted inequalities for potential and fractional type maximal operators. Indiana Univ. Math. J. 43, 663–683 (1994)MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    Rao M., Ren Z.: Theory of Orlicz Spaces. Dekker, New York (1991)MATHGoogle Scholar
  10. 10.
    Iida T., Sato E., Sawano Y., Tanaka H.: Multilinear fractional integrals on Morrey spaces. Acta Math. Sin. (to appear)Google Scholar
  11. 11.
    Sawano Y., Sugano S., Tanaka H.: Orlicz-Morrey spaces and fractional operators. Potential Anal. (to appear)Google Scholar
  12. 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)MathSciNetMATHGoogle Scholar
  13. 13.
    Tang L.: Endpoint estimates for multilinear fractional integrals. J. Aust. Math. Soc. 84, 419–429 (2008)MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  • Takeshi Iida
    • 1
  • Enji Sato
    • 1
  • Yoshihiro Sawano
    • 2
  • Hitoshi Tanaka
    • 3
  1. 1.Department of Mathematical Sciences, Faculty of ScienceYamagata UniversityYamagataJapan
  2. 2.Department of MathematicsKyoto UniversityKyotoJapan
  3. 3.Graduate School of Mathematical SciencesThe University of TokyoTokyoJapan

Personalised recommendations