Doklady Mathematics

, Volume 94, Issue 2, pp 558–560 | Cite as

Sublinear operators in generalized weighted Morrey spaces

  • V. KokilashviliEmail author
  • A. Meskhi
  • H. Rafeiro


Generalized weighted Morrey spaces defined on spaces of homogeneous type are introduced by using weight functions in the Muckenhoupt class. Theorems on the boundedness of a large class of sublinear operators on these spaces are presented. The classes of sublinear operators under consideration contain a whole series of important operators of harmonic analysis, such as, e.g., maximal functions, singular and fractional integrals, Bochner–Riesz means, and so on.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Y. Komori and S. Shirai, Math. Nachr. 282 (2), 219–231 (2009).MathSciNetCrossRefGoogle Scholar
  2. 2.
    S. Shi, Z. Fu, and F. Zhao, J. Ineq. Appl. Art. 2013–2390 (2013).Google Scholar
  3. 3.
    R. R. Coifman and G. Weiss, Analyse harmonique noncommutative sur certains espaces homogénes (Springer-Verlag, Berlin, 1971).CrossRefzbMATHGoogle Scholar
  4. 4.
    J.-O. Strömberg and A. Torchinsky, Weighted Hardy Spaces (Springer-Verlag, Berlin, 1989).CrossRefzbMATHGoogle Scholar
  5. 5.
    T. Iwaniec and C. Sbordone, Arch. Ration. Mech. Anal. 119 (2), 129–143 (1992).MathSciNetCrossRefGoogle Scholar
  6. 6.
    L. Greco, T. Iwaniec, and C. Sbordone, Manuscr. Math. 92 (2), 249–258 (1997).MathSciNetCrossRefGoogle Scholar
  7. 7.
    A. Meskhi, Complex Var. Elliptic Equations 56 (10/11), 1003–1019 (2011).MathSciNetCrossRefGoogle Scholar
  8. 8.
    H. Rafeiro, in Advances in Harmonic Analysis and Operator Theory (Birkhäuser, Basel, 2013), pp. 349–356.CrossRefzbMATHGoogle Scholar
  9. 9.
    B. Muckenhoupt, Studia Math. 44, 31–38 (1972).MathSciNetGoogle Scholar
  10. 10.
    B. Muckenhoupt and R. Wheeden, Trans. Am. Math. Soc. 192, 261–274 (1974).MathSciNetCrossRefGoogle Scholar
  11. 11.
    D. E. Edmunds, V. Kokilashvili, and A. Meskhi, Bounded and Compact Integral Operators (Kluwer, Dordrecht, 2002).CrossRefzbMATHGoogle Scholar
  12. 12.
    A. Meskhi, Proc. Razmadze Math. Inst. 169, 119–132 (2015).MathSciNetGoogle Scholar
  13. 13.
    V. Kokilashvili and A. Meskhi, Lith. Math. J. 53 (1), 27–39 (2013).MathSciNetCrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2016

Authors and Affiliations

  1. 1.Razmadze Mathematical InstituteJavakhishvili Tbilisi State UniversityTbilisiGeorgia
  2. 2.Pontificia Universidad JaverianaBogotáColombia

Personalised recommendations