Analysis Mathematica

, Volume 25, Issue 1, pp 179–186 | Cite as

A weak type inequality for generalized maximal operators on spaces of homogeneous type

  • Byung-Oh Park
  • Бун-О Парк


A condition is given for a certain generalized maximal operator to be of weak type (ps, qs), where 1≤pq<∞, 1≤s<∞. This operator unifies various results about the Poisson integral operators cited in the literature.


Получено условие, для того чтобы некоторый обобшонно максимальный оператор имел слабый тип (ps, qs), 1≤p,q,s<∞. Этот оператор унифицирует раэличные реэультаты об интегральных операторах Пуассона, имеюшиеся в цитируемой литературе.


Hardy Space Maximal Operator Maximal Function Weak Type Carleson Measure 
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.

Неравенство слабого типа для максимальных операторов в однородных пространствах


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [C]
    L. Carleson, Interpolation by bounded analytic functions and the corona problem,Ann. Math.,76(1962), 547–559.CrossRefMathSciNetGoogle Scholar
  2. [CW]
    R. R. Coifman andG. Weiss, Extensions of Hardy spaces and their uses in analysis,Bull. Amer. Math. Soc.,83(1977), 569–645.MATHCrossRefMathSciNetGoogle Scholar
  3. [FS]
    C. Fefferman andE. M. Stein, Some maximal inequalities,Amer. J. Math.,93(1971), 107–115.MATHCrossRefMathSciNetGoogle Scholar
  4. [M]
    B. Mukenhoupt, Weighted norm inequalities for the Hardy maximal function,Trans. Amer. Math. Soc.,165(1972), 115–121.Google Scholar
  5. [R]
    F. J. Ruiz, A unified approach to Carleson measures andA p weights,Pacific J. Math.,117(1985), 397–404.MATHMathSciNetGoogle Scholar
  6. [RT]
    F. J. Ruiz andJ. L. Torrea, A unified approach to Carleson measures andA p weights. II,Pacific J. Math.,120(1985), 189–197.MATHMathSciNetGoogle Scholar
  7. [GcRf]
    J. Garcia-Cuerva andJ. L. Rubio De Francia,Weighted norm inequalities and related topics, North-Holland (Amsterdam, 1985).MATHGoogle Scholar
  8. [S]
    E. M. Stein,Harmonic analysis: real variable methods, orthogonality, and oscillatory integrals,, Princeton Univ. Press (Princeton, N.J., 1993).MATHGoogle Scholar
  9. [Su]
    J. Sueiro, On maximal functions and Poisson-Szegő integrals,Trans. Amer. Math. Soc.,298(1986), 653–669.MATHCrossRefMathSciNetGoogle Scholar
  10. [W]
    P. Wejie, Weighted norm inequalities for certain maximal operator with approach region,Lecture Notes in Math.,1494, Springer (Berlin, 1988) 169–175.Google Scholar

Copyright information

© Akadémiai Kiadó 1999

Authors and Affiliations

  • Byung-Oh Park
    • 1
    • 2
  • Бун-О Парк
    • 1
    • 2
  1. 1.Chang Shin APT 109-805Mang Tyung-Dong, Young ChunKyungbukKorea (South)
  2. 2.Department of MathematicsKyungbuk National UniversityKorea

Personalised recommendations