A Class of Weighted Inequalities

  • Salah A. A. Emara
Conference paper


Given indices p and q, 1 ≤ p, q ≤ ∞, T a quasilinear operator bounded between weighted interpolation Awi,qi to Bwi,qi-spaces, i = 0, 1, 1 ≤ q i,q i ≤ ∞, where w, w are weight functions belonging to some class of functions BK. We give conditions on pairs of functions u and v which are sufficient that Mathtype holds, where C is a constant independent of f and K (.,.;.) is the Peetre K-functional.


Weight Condition Hardy Inequality Weight Class Norm Inequality Weight Norm Inequality 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    K.F. Andersen and B. Muckenhoupt; Weighted weak type Hardy inequalities with applications to Hilbert transform and maximal functions; Studia Math. 72 (1982), 9–26.MathSciNetMATHGoogle Scholar
  2. 2.
    J.S. Bradley; Hardy inequalities with mixed norms; Canad. Math. Bull. 21 (1978), 405–408.MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    A.P. Calderon and R. Scott; Sobolev type inequalities for p O; Studia Math. 62 (1978), 73–92.MathSciNetGoogle Scholar
  4. 4.
    J. Gustavsson; A function parameter in connection with interpolation of Banach spaces; Math. Scand. 42 (1978), 289–305.MathSciNetMATHGoogle Scholar
  5. 5.
    H.P. Heinig; Interpolation of quasi-normed spaces involving weights; Canad. Math. Soc. Conf. Proc. Vol. 1, 1980 Seminar on Harmonic Analysis, 245–267, 1981.Google Scholar
  6. 6.
    H.P. Heinig; Weighted norm inequalities for certain integral operators II; Proc. Amer. Math. Soc. (3) 95 (1985), 387–396.MathSciNetMATHCrossRefGoogle Scholar
  7. 7.
    T.F. kalugina; Interpolation of Banach spaces with functional parameter. The Reiteraction theorem; Vestnik Moskovskoyo University, Ser.l, Math. Mech. 30 (6) (1975), 68–77 (Engl. Transl. Moscow University Math. Bull. 30 (6) (1975), 108–116 ).MathSciNetMATHGoogle Scholar
  8. 8.
    W. Mazja; Einbettungassätze für Sobolevsche Raume; Teil 1, Teubner Texte zur Math., Teubner Verl. Leipzig (1979).Google Scholar
  9. 9.
    E. Sawyer; Weighted Lebesgue and Lorentz norm inequalities for the Hardy operators; Trans. A.M.S. 281 (1) (1984), 329–337.MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Tokyo 1991

Authors and Affiliations

  • Salah A. A. Emara
    • 1
  1. 1.Department of Science Mathematics UnitThe American University in CairoCairoEgypt

Personalised recommendations