Annali di Matematica Pura ed Applicata

, Volume 189, Issue 3, pp 523–538 | Cite as

Hölder type inequalities in Lorentz spaces

  • Viktor Kolyada
  • Javier Soria


We study optimal Hölder type inequalities for the Lorentz spaces L p,s(R, μ), in the range 1 < p < ∞, 1 ≤ s ≤ ∞, for both the maximal and the dual norms. These estimates also give sharp results for the corresponding associate norms.


Equivalent norms Level function Lorentz spaces Sharp constants 

Mathematics Subject Classification (2000)

46E30 46B25 


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  1. 1.
    Barza S., Kolyada V., Soria J.: Sharp constants related to the triangle inequality in Lorentz spaces. Trans. Am. Math. Soc. 361, 5555–5574 (2009)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Bennett C., Sharpley R.: Interpolation of Operators. Academic Press, Boston (1988)zbMATHGoogle Scholar
  3. 3.
    Carro, M.J., Raposo, J.A., Soria, J.: Recent Developments in the Theory of Lorentz Spaces and Weighted Inequalities. In: Mem. Am. Math. Soc, vol. 187. Providence (2007)Google Scholar
  4. 4.
    Halperin I.: Function spaces. Can. J. Math. 5, 273–288 (1953)zbMATHMathSciNetGoogle Scholar
  5. 5.
    Kolyada V.I.: Inequalities of Gagliardo–Nirenberg type and estimates for the moduli of continuity. Russ. Math. Surv. 60, 1147–1164 (2005)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Lorentz G.G.: On the theory of spaces Λ. Pac. J. Math. 1, 411–429 (1951)zbMATHMathSciNetGoogle Scholar
  7. 7.
    Lorentz G.G.: Bernstein Polynomials. University of Toronto Press, Toronto (1953)zbMATHGoogle Scholar
  8. 8.
    Sinnamon G.: Spaces defined by the level function and their duals. Stud. Math. 111, 19–52 (1994)zbMATHMathSciNetGoogle Scholar
  9. 9.
    Stein E.M.: Singular Integrals and Differentiability Properties of Functions. Princeton University Press, Princeton (1970)zbMATHGoogle Scholar
  10. 10.
    Stein E.M., Weiss G.: Introduction to Fourier Analysis on Euclidean Spaces. Princeton University Press, Princeton (1971)zbMATHGoogle Scholar

Copyright information

© Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag 2009

Authors and Affiliations

  1. 1.Department of MathematicsKarlstad UniversityKarlstadSweden
  2. 2.Department of Applied Mathematics and AnalysisUniversity of BarcelonaBarcelonaSpain

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