Annali di Matematica Pura ed Applicata

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

Hölder type inequalities in Lorentz spaces

Article

Abstract

We study optimal Hölder type inequalities for the Lorentz spaces Lp,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.

Keywords

Equivalent norms Level function Lorentz spaces Sharp constants 

Mathematics Subject Classification (2000)

46E30 46B25 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  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)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Bennett C., Sharpley R.: Interpolation of Operators. Academic Press, Boston (1988)MATHGoogle 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)MATHMathSciNetGoogle 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)MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Lorentz G.G.: On the theory of spaces Λ. Pac. J. Math. 1, 411–429 (1951)MATHMathSciNetGoogle Scholar
  7. 7.
    Lorentz G.G.: Bernstein Polynomials. University of Toronto Press, Toronto (1953)MATHGoogle Scholar
  8. 8.
    Sinnamon G.: Spaces defined by the level function and their duals. Stud. Math. 111, 19–52 (1994)MATHMathSciNetGoogle Scholar
  9. 9.
    Stein E.M.: Singular Integrals and Differentiability Properties of Functions. Princeton University Press, Princeton (1970)MATHGoogle Scholar
  10. 10.
    Stein E.M., Weiss G.: Introduction to Fourier Analysis on Euclidean Spaces. Princeton University Press, Princeton (1971)MATHGoogle 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

Personalised recommendations