Acta Mathematica Sinica, English Series

, Volume 29, Issue 5, pp 883–896 | Cite as

Estimates for vector-valued commutators on weighted Morrey space and applications



In this paper, we introduce weighted vector-valued Morrey spaces and obtain some estimates for vector-valued commutators on these spaces. Applications to Calderón-Zygmund singular integral operators, oscillatory singular integral operators and parabolic difference equations are considered.


Weighted Morrey space vector-valued commutator Ap weights 

MR(2010) Subject Classification

42B20 42B25 


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Supplementary material

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  1. [1]
    Lu, S., Ding, Y., Yan, D.: Singular Integrals and Related Topics, World Sci, Singapore, 2007MATHCrossRefGoogle Scholar
  2. [2]
    Benedek, A., Calderòn, A., Panzone, R.: Convolution operators on Banach space valued functions. Proc. Nat. Acad. Sci. USA, 48, 356–365 (1962)MATHCrossRefGoogle Scholar
  3. [3]
    Garcia-Cuerva, J., Rubio de Francia, J.: Weighted Norm Inequalities and Related Topics, Amsterdam, North-Holland, 1985Google Scholar
  4. [4]
    Bloom, S.: A commutator theorem and weighted BMO. Trans. Amer. Math. Soc., 292, 103–122 (1985)MathSciNetMATHCrossRefGoogle Scholar
  5. [5]
    Segovia, C., Torrea, J.: Vector valued commutators and applications. Indiana Univ. Math. J., 38, 959–971 (1989)MathSciNetMATHCrossRefGoogle Scholar
  6. [6]
    Morrey, C.: On the solutions of quasi-linear elliptic partial differential equations. Trans. Amer. Math. Soc., 43, 126–166 (1938)MathSciNetCrossRefGoogle Scholar
  7. [7]
    Adams, D.: A note on Riesz potentials. Duke Math. J., 42, 765–778 (1975)MathSciNetMATHCrossRefGoogle Scholar
  8. [8]
    Chiarenza, F., Frasca, M.: Morrey spaces and Hardy-Littlewood maximal function. Rend. Math. Appl., 7(7), 273–279 (1987)MathSciNetMATHGoogle Scholar
  9. [9]
    Duong, X., Xiao, J., Yan, L.: Old and new Morrey spaces with heat kernel bounds. J. Fourier Anal. Appl., 13, 87–111 (2007)MathSciNetMATHCrossRefGoogle Scholar
  10. [10]
    Lin, H., Nakai, H., Yang, D.: Boundedness of Lusin-area and g γ* functions on localized Morrey-Campanato spaces over doubling metric measure spaces. J. Funct. Spaces Appl., 9(3), 245–282 (2011)MathSciNetMATHCrossRefGoogle Scholar
  11. [11]
    Nakai, E.: The Cmapanato, Morrey and Hölder spaces on spaces of homogeneous type. Studia Math., 176, 1–19 (2006)MathSciNetMATHCrossRefGoogle Scholar
  12. [12]
    Komori, Y., Shirai, S.: Weighted Morrey spaces and a singular integral operator. Math. Nachr., 282, 219–231 (2009)MathSciNetMATHCrossRefGoogle Scholar
  13. [13]
    Ding, Y.: A characterization of BMO via commutators for some operators. Northeast Math., 13, 422–432 (1997)MathSciNetMATHGoogle Scholar
  14. [14]
    Rubio de Francia, J., Ruiz, J., Torrea, F.: Calderòn-Zygmund theory for operator-valued kernels. Adv. Math., 62, 7–48 (1986)MathSciNetMATHCrossRefGoogle Scholar
  15. [15]
    Ricci, F., Stein, E.: Harmonic analysis on nilpotant groups and singular integrals I: oscillatory integrals. J. Funct. Anal., 73, 179–194 (1987)MathSciNetMATHCrossRefGoogle Scholar
  16. [16]
    Chanillo, S., Christ, M.: Weak (1,1) bounds for oscillatory integrals. Duke. Math. J., 55, 141–155 (1987)MathSciNetMATHCrossRefGoogle Scholar
  17. [17]
    Fu, Z., Lu, S., Sato, S., et al.: On weighted weak type norm inequalities for one-sided oscillatory singular integrals. Studia Math., 207, 137–151 (2011)MathSciNetMATHCrossRefGoogle Scholar
  18. [18]
    Lu, S., Zhang, Y.: Weighted norm inequality of a class of oscillatory singular operators. Chin. Sci. Bull., 37, 9–13 (1992)MATHGoogle Scholar
  19. [19]
    Sato, S.: Weighted weak type (1,1) estimates for oscillatory singular integrals. Studia Math., 47, 1–17 (2001)CrossRefGoogle Scholar
  20. [20]
    Shi, S., Fu, Z., Lu, S.: Weighted estimates for commutators of one-sided oscillatory integral operators. Front. Math. China, 6(3), 507–516 (2011)MathSciNetCrossRefGoogle Scholar
  21. [21]
    Lu, S.: A class of oscillatory integrals. Int. J. Appl. Math. Sci., 2(1), 42–58 (2005)Google Scholar
  22. [22]
    Hunt, R.: On the convergence of Fourier series, Orthogonal Expansions and their Continuous Analogues, Proc. Conf., Edwardsville(1967), Southern Illinois Univ. Press, Carbondale, 1968, 235–255Google Scholar
  23. [23]
    Ruiz, F., Torrea, J.: Parabolic differential equations and vector-valued Fourier analysis. Colloquium Math., 1, 61–75 (1989)MathSciNetGoogle Scholar

Copyright information

© Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.School of ScienceLinyi UniversityLinyiP. R. China
  2. 2.School of Mathematical SciencesBeijing Normal UniversityBeijingP. R. China

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