Advertisement

Dual spaces of local Morrey-type spaces

  • Amiran GogatishviliEmail author
  • Rza Mustafayev
Article

Abstract

In this paper we show that associated spaces and dual spaces of the local Morrey-type spaces are so called complementary local Morrey-type spaces. Our method is based on an application of multidimensional reverse Hardy inequalities.

Keywords

local Morrey-type spaces complementary local Morrey-type spaces associated spaces dual spaces multidimensional reverse Hardy inequalities 

MSC 2010

46E30 26D15 

References

  1. [1]
    V. I. Burenkov, H.V. Guliyev: Necessary and sufficient conditions for boundedness of the maximal operator in the local Morrey-type spaces. Stud. Math. 163 (2004), 157–176.MathSciNetzbMATHCrossRefGoogle Scholar
  2. [2]
    V. I. Burenkov, H.V. Guliyev, V. S. Guliyev: On boundedness of the fractional maximal operator from complementary Morrey-type spaces to Morrey-type spaces. The Interaction of Analysis and Geometry. International School-Conference on Analysis and Geometry, Novosibirsk, Russia, August 23–September 3, 2004. American Mathematical Society (AMS), Providence; Contemporary Mathematics 424 (2007), 17–32.MathSciNetGoogle Scholar
  3. [3]
    V. I. Burenkov, H.V. Guliyev, V. S. Guliyev: Necessary and sufficient conditions for boundedness of fractional maximal operators in local Morrey-type spaces. J. Comput. Appl. Math. 208 (2007), 280–301.MathSciNetzbMATHCrossRefGoogle Scholar
  4. [4]
    V. I. Burenkov, H.V. Guliyev, T.V. Tararykova, A. Serbetci: Necessary and sufficient conditions for the boundedness of genuine singular integral operators in the local Morrey-type spaces. Dokl. Math. 78 (2008), 651–654; Translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 422 (2008), 11–14.MathSciNetzbMATHCrossRefGoogle Scholar
  5. [5]
    V. I. Burenkov, V. S. Guliyev: Necessary and sufficient conditions for the boundedness of the Riesz potential in local Morrey-type spaces. Potential Anal. 30 (2009), 211–249.MathSciNetzbMATHCrossRefGoogle Scholar
  6. [6]
    V. I. Burenkov, A. Gogatishvili, V. S. Guliyev, R.Ch. Mustafayev: Boundedness of the fractional maximal operator in Morrey-type spaces. Complex Var. Elliptic Equ. 55 (2010), 739–758.MathSciNetzbMATHCrossRefGoogle Scholar
  7. [7]
    W.D. Evans, A. Gogatishvili, B. Opic: The reverse Hardy inequality with measures. Math. Inequal. Appl. 11 (2008), 43–74.MathSciNetzbMATHGoogle Scholar
  8. [8]
    A. Gogatishvili, R. Mustafayev: The multidimensional reverse Hardy inequalities. Math. Inequal. & Appl. 14 (2011). Preprint, Institute of Mathematics, AS CR, Prague 2009-5-27. Available at http://www.math.cas.cz/preprint/pre-179.pdf.
  9. [9]
    V. S. Guliyev: Integral operators on function spaces on the homogeneous groups and on domains in ℝn. Doctor’s degree dissertation. Mat. Inst. Steklov, Moscow, 1994. (In Russian.)Google Scholar
  10. [10]
    V. S. Guliyev: Function Spaces, Integral Operators and Two Weighted Inequalities on Homogeneous Groups. Some Applications. Baku, 1999. (In Russian.)Google Scholar
  11. [11]
    V. S. Guliyev, R.Ch. Mustafayev: Integral operators of potential type in spaces of homogeneous type. Dokl. Math. 55 (1997), 427–429; Translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 354 (1997), 730–732.Google Scholar
  12. [12]
    V. S. Guliyev, R.Ch. Mustafayev: Fractional integrals on spaces of homogeneous type. Anal. Math. 24 (1998), 1810–200. (In Russian.)Google Scholar

Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2011

Authors and Affiliations

  1. 1.PrahaCzech Republic
  2. 2.BakuAzerbaijan
  3. 3.Institute of Mathematics of the Academy of Sciences of the Czech RepublicPraha 1Czech Republic
  4. 4.Institute of Mathematics and MechanicsAcademy of Sciences of AzerbaijanBakuAzerbaijan
  5. 5.Department of Mathematics, Faculty of Science and ArtsKirikkale UniversityYahsihan, KirikkaleTurkey

Personalised recommendations