Acta Mathematica Sinica

, Volume 21, Issue 6, pp 1535–1544 | Cite as

Morrey Spaces for Non–doubling Measures



The authors give a natural definition of Morrey spaces for Radon measures which may be non–doubling but satisfy certain growth condition, and investigate the boundedness in these spaces of some classical operators in harmonic analysis and their vector–valued extension.


Morrey space non–doubling measure vector–valued 

MR (2000) Subject Classification

42B35 42B25 


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  1. 1.
    Gilberg, D., Trudinger, N. S.: Elliptic Partial Differential Equations of Second Order, 2nd ed., Springer– Verlag, Berlin, 1983Google Scholar
  2. 2.
    García–Cuerva, J., Rubio de Francia, J. L.: Weighted Norm Inequalities and Related Topics. North–Holland Math. Stud., 116, (1985)Google Scholar
  3. 3.
    Stein, E. M.: Harmonic Analysis: Real–Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton Univ. Press, 1993Google Scholar
  4. 4.
    Nazarov, F., Treil, S., Volberg, A.: Weak type estimates and Cotlar inequalities for Calderón–Zygmund operators on nonhomogeneous spaces, Internat. Math. Res. Notices 463–487, 1998Google Scholar
  5. 5.
    Tolsa, X.: Littlewood–Paley theory and the T(1) theorem with non–doubling measures. Adv. Math., 164, 57–116 (2001)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Tolsa, X.: BMO, H 1, and Calderón–Zygmund operators for non doubling measures. Math. Ann., 319, 89–149 (2001)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Han, Y., Yang, D.: Triebel–Lizorkin spaces for non doubling measures. Studia Math., 164, 105–140 (2004)Google Scholar
  8. 8.
    Deng, D., Han, Y., Yang, D.: Besov spaces with non doubling measures. Trans. Amer. Math. Soc., to appearGoogle Scholar
  9. 9.
    Adams, D.: A note on Riesz potentials. Duke Math. J., 42, 765–778 (1975)CrossRefMathSciNetGoogle Scholar
  10. 10.
    Chiarenza, F., Frasca, M.: Morrey spaces and Hardy–Littlewood maximal function. Rend. Mat., 7, 273–279 (1987)MathSciNetGoogle Scholar
  11. 11.
    Komori, Y.: Calderón–Zygmund operators on the predual of a Morrey space. Acta Mathematica Sinica, English Series, 19(2), 297–302 (2003)CrossRefMathSciNetGoogle Scholar
  12. 12.
    Sawano, Y.: Sharp estimates of the modified Hardy–Littlewood maximal operator on the nonhomogeneous space via covering lemmas. Hokkaido Math. J., 34, 435–458 (2005)MathSciNetGoogle Scholar
  13. 13.
    García–Cuerva, J., Gatto, E.: Boundedness properties of fractional integral operators associated to nondoubling measures. Studia Math., 162(3), 245–261 (2004)MathSciNetGoogle Scholar
  14. 14.
    Chen, W., Sawyer, E.: A note on commutators of fractional integrals with RBMO(μ) functions. Illinois J. Math., 46(4), 1287–1298 (2002)MathSciNetGoogle Scholar
  15. 15.
    García–Cuerva, J., Martell, J. M.: Weighted inequalities and vector–valued Calderón–Zygmund operators on nonhomogeneous spaces. Publ. Mat., 44(2), 613–640 (2000)MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.Graduate School of Mathematical SciencesThe University of TokyoMeguro–ku Tokyo 153–8914Japan

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