Advertisement

Norm Inequalities for Generalized Fractional Integral Operators

  • J. C. Kuang
Chapter
Part of the Springer Optimization and Its Applications book series (SOIA, volume 151)

Abstract

Some new norms of the integral operator with the radial kernel on n-dimensional vector spaces are deduced. These norms used then to establish some new norm inequalities for generalized fractional integral operators and the Riesz potential operators.

2010 AMS Mathematics Subject Classification Codes

47A30; 47A63 

References

  1. 1.
    A. Akbulut, V.H. Hamzayev, Z.V. Safarov, Boundedness of rough fractional multilinear integral operators on generalized Morrey spaces. J. Inequal. Appl. 234 (2015)Google Scholar
  2. 2.
    B.E.J. Dahlberg, Regularity properties of Riesz potentials. Indiana Univ. Math. J. 28(2), 257–268 (1979)MathSciNetCrossRefGoogle Scholar
  3. 3.
    E. DiBenedetto, Real Analysis (Birkhäuser, Boston, 2002)CrossRefGoogle Scholar
  4. 4.
    E. Eridani, On the boundedness of a generalized fractional integral on generalized Morrey spaces. Tamkang J. Math. 33(4), 335–340 (2002)MathSciNetzbMATHGoogle Scholar
  5. 5.
    G.H. Hardy, J.E. Littlewood, G. Pólya, The maximum of a certain bilinear form. Proc. Lond. Math. Soc. 2–25, 265–282 (1926)MathSciNetCrossRefGoogle Scholar
  6. 6.
    G.H. Hardy, J.E. Littlewood, On certain inequalities connected with the calculus of variations. J. Lond. Math. Soc. 5, 34–39 (1930)CrossRefGoogle Scholar
  7. 7.
    J.C. Kuang, Applied Inequalities, 4th edn. (Shandong Science and Technology Press, Jinan, 2010)Google Scholar
  8. 8.
    J.C. Kuang, Real and Functional Analysis (Continuation), vol. 2 (Higher Education Press, Beijing, 2015)Google Scholar
  9. 9.
    J.C. Kuang, Multiple weighted Orlicz spaces and applications, in Contributions in Mathematics and Engineering in Honor of Constantin Carathéodory, Chapter 18, ed. by P.M. Pardalos, T.M. Rassias (Springer, Berlin, 2016)CrossRefGoogle Scholar
  10. 10.
    J.C. Kuang, Riesz potential operator norm inequalities and its generalizations. Acta Anal. Funct. Appl. 19(1), 33–47 (2017)MathSciNetzbMATHGoogle Scholar
  11. 11.
    K. Kurata, S. Nishigaki, S. Sugano, Boundedness of integral operators on generalized Morrey spaces and its application to Schrödinger operators. Proc. Am. Math. Soc. 128, 1125–1134 (1999)CrossRefGoogle Scholar
  12. 12.
    E.H. Lieb, Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities. Ann. Math. 118, 349–374 (1983)MathSciNetCrossRefGoogle Scholar
  13. 13.
    E.H. Lieb, M. Loss, Analysis, 2nd edn. (American Mathematical Society, Providence, 2001)zbMATHGoogle Scholar
  14. 14.
    E. Nakai, Hardy-Littlewood maximal operator, singular integral operators, and the Riesz potentials on generalized Morrey spaces. Math. Nachr. 166, 95–103 (1994)MathSciNetCrossRefGoogle Scholar
  15. 15.
    E. Nakai, On generalized fractional integrals. Taiwan. J. Math. 5, 587–602 (2001)MathSciNetCrossRefGoogle Scholar
  16. 16.
    S.L. Sobolev, On a theorem of functional analysis. Mat. Sb. (N.S.) 4, 471–479 (1938)Google Scholar
  17. 17.
    E.M. Stein, G. Weiss, Fractional integrals in n-dimensional Euclidean space. J. Math. Mech. 7, 503–514 (1958)MathSciNetzbMATHGoogle Scholar
  18. 18.
    B.C. Yang, L. Debnath, Half-discrete Hilbert-type inequalities (World Scientific, Singapore, 2014)CrossRefGoogle Scholar
  19. 19.
    D. Zwillinger, Handbook of Integration (Springer, New York, 1992)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • J. C. Kuang
    • 1
  1. 1.Department of MathematicsHunan Normal UniversityChangshaPeople’s Republic of China

Personalised recommendations