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The Journal of Geometric Analysis

, Volume 27, Issue 1, pp 120–141 | Cite as

Two-Weight Norm Inequalities for the Local Maximal Function

  • M. Ramseyer
  • O. Salinas
  • B. Viviani
Article
  • 123 Downloads

Abstract

For a local maximal function defined on a certain family of cubes lying “well inside” of \(\Omega \), a proper open subset of \({\mathbb {R}}^n\), we characterize the couple of weights (uv) for which it is bounded from \(L^p(v)\) on \(L^q(u)\).

Keywords

Bounded Mean Oscillation Fractional Integral Variable Exponent 

Mathematics Subject Classification

Primary 42B35 

Notes

Acknowledgments

This research is partially supported by Grants from Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET) and Facultad de Ingeniería Química Universidad Nacional del Litoral (UNL), Argentina.

References

  1. 1.
    Cruz-Uribe, D.: New proofs of two-weight norm inequalities for the maximal operator. Georg. Math. J. 7(1), 33–42 (2000)MathSciNetzbMATHGoogle Scholar
  2. 2.
    García-Cuerva, J., Rubio de Francia, J.L.: Weighted norm inequalities and related topics. North-Holland Mathematics Studies, vol. 116. North-Holland Publishing Co, Amsterdam (1985)Google Scholar
  3. 3.
    Harboure, E., Salinas, O., Viviani, B.: Local maximal function and weights in a general setting. Math. Ann. 358(3–4), 609–628 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Jawerth, B.: Weighted inequalities for maximal operators: linearization, localization and factorization. Am. J. Math. 108(2), 361–414 (1986)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Muckenhoupt, B.: Weighted norm inequalities for the Hardy maximal function. Trans. Am. Math. Soc. 165, 207–226 (1972)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Pérez, C.: Two weighted norm inequalities for Riesz potentials and uniform \(L^p\)-weighted Sobolev inequalities. Indiana Univ. Math. J. 39(1), 31–44 (1990)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Sawyer, E.: A characterization of a two-weight norm inequality for maximal operators. Stud. Math. 75(1), 1–11 (1982)MathSciNetzbMATHGoogle Scholar
  8. 8.
    Sawyer, E.: Weighted norm inequalities for fractional maximal operators. CMS Conf. Proc. 1, 283–309 (1980)MathSciNetGoogle Scholar

Copyright information

© Mathematica Josephina, Inc. 2016

Authors and Affiliations

  1. 1.Instituto de Matemática Aplicada del Litoral, FIQUNL, CONICETSanta FeArgentina

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