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Periodica Mathematica Hungarica

, Volume 44, Issue 1, pp 101–110 | Cite as

Two-weight norm inequalities for fractional maximal operators on spaces of generalized homogeneous type

  • R. Trujillo-González
Article

Abstract

In this paper a characterization is given for a pairs of weights (w,v) for which the fractional maximal operator is bounded from \(L^\user1{p} (X,\user1{vd}\mu )\) when is a space of generalized homogeneous type introduced by A. Carbery et al. [4].

Keywords

Maximal Operator Homogeneous Type Norm Inequality Fractional Maximal Operator 
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.

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REFERENCES

  1. [1]
    A. BERNARDIS and O. SALINAS, Two-weight norm inequalities for the fractional maximal operator on spaces of homogeneous type, Studia Math. 108 (3) (1994), 201–207.Google Scholar
  2. [2]
    M. CHRIST, Lectures on Singular Integral Operators, Regional Conferences Series in Mathematics, no. 77, 1990.Google Scholar
  3. [3]
    R. COIFMAN and G. WEISS, Analyse harmonique non-commutative sur certains espaces homogènes, Lecture Notes in Math. 242, Springer-Verlag, Berlin, 1971.Google Scholar
  4. [4]
    A. CARBERY, J. VANCE, S. WAINGER and J. WRIGHT, A variant of the notion of a space of homogeneous type, J. Funct. Anal. 132 (1995), 119–140.Google Scholar
  5. [5]
    A. GOGATISHVILI and V. KOKILASHVILI, Criteria of strong type two-weighted inequalities for fractional maximal functions, Georgian Math. J. 3 (5) (1996), 423–446.Google Scholar
  6. [6]
    B. JAWERTH, Weighted inequalities for maximal operators: linearization, localization and factorization, Amer. J. Math. 108 (1986), 361–414.Google Scholar
  7. [7]
    A. KORáNYI and S. VáGI, Singular integrals in homogenous spaces and some problems from classical analysis, Ann. Scuola Norm. Sup. Pisa (3) 25 (1971), 575–648.Google Scholar
  8. [8]
    C. PéREZ, Weighted norm inequalities for general maximal operators, Publ. Mat. 35 (1991), 169–186.Google Scholar
  9. [9]
    LAI QINSHENG, The sharp maximal function on spaces of generalized homogeneous type, J. Funct. Anal. 150 (1997), 75–100.Google Scholar
  10. [10]
    E. T. SAWYER, A characterization of a two-weight norm inequality for maximal operators, Studia Math. 75 (1) (1982), 1–11.Google Scholar
  11. [11]
    J. O. STRöMBERG and A. TORCHINSKY, Weighted Hardy Spaces, Lecture Notes in Math. 1381, Springer-Verlag, Berlin, 1989.Google Scholar
  12. [12]
    E. M. STEIN and G. WEISS, Introduction to Fourier Analysis on Euclidean Spaces, Princeton University Press, New Jersey, 1975.Google Scholar
  13. [13]
    R. L. WHEEDEN, A characterization of some weighted norm inequalities for the fractional maximal function, Studia Math. 107 (3) (1993), 257–272.Google Scholar

Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • R. Trujillo-González
    • 1
  1. 1.Departamento de Análisis MatemáticoUniversidad de La LagunaTenerifeSpain

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