Weighted Lebesgue and \(BMO^\gamma \) norm inequalities for the Calderón and Hilbert operators

  • Elida V. Ferreyra
  • Guillermo J. FloresEmail author
  • Beatriz E. Viviani


Necessary and sufficient conditions are given for generalized Calderón and Hilbert operators to be bounded from weighted Lebesgue spaces into suitable weighted BMO and Lipschitz spaces. Moreover, we have obtained new results on the boundedness of these operators from \(L^{\infty }\) into BMO, even in the unweighted case for the Hilbert operator. The class of weights involved are close to the doubling and reverse Hölder conditions related to the Muckenhoupt’s classes.


Calderón operator BMO spaces Weighted inequalities Integral operators 

Mathematics Subject Classification

30H35 42B25 42B35 



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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Elida V. Ferreyra
    • 1
  • Guillermo J. Flores
    • 1
    Email author
  • Beatriz E. Viviani
    • 2
  1. 1.CIEM-FaMAFUniversidad Nacional de CórdobaCórdobaArgentina
  2. 2.IMAL and FIQUniversidad Nacional del LitoralSanta FeArgentina

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