Advertisement

A note on choquet integrals with respect to Hausdorff capacity

  • David R. Adams
Contributed Papers
Part of the Lecture Notes in Mathematics book series (LNM, volume 1302)

Keywords

Morrey Space Minimax Theorem Riesz Potential Dyadic Cube Distributional Derivative 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. [1]
    D. Adams, A note on Riesz potentials, Duke Math. J. 42 (1975), 765–778.CrossRefzbMATHMathSciNetGoogle Scholar
  2. [2]
    ____, Sets and functions of finite capacity, Ind. U. Math. J. 27 (1978), 611–627.CrossRefzbMATHGoogle Scholar
  3. [3]
    ____, L p-capacity integrals with some applications, Proc. Symp. Pure Math. A.M.S. 35 (1979), 359–367.CrossRefGoogle Scholar
  4. [4]
    B. Anger, Representations of capacities, Math. Ann. 229 (1977), 245–258.CrossRefzbMATHMathSciNetGoogle Scholar
  5. [5]
    L. Carleson, Selected problems in exceptional sets, Van Norstrand 1967.Google Scholar
  6. [6]
    G. Choquet, Theory of capacities, Ann. Inst. Fourier, 5 (1953), 131–295.CrossRefMathSciNetGoogle Scholar
  7. [7]
    ____, Forme abstraite du théoréme de capacitabilitié, loc.cit., 9 (1959), 83–89.CrossRefzbMATHMathSciNetGoogle Scholar
  8. [8]
    K. Fan, Minimax theorems, Proc. Nat. Acad. Sci. U.S.A. 39 (1953), 42–47.CrossRefzbMATHMathSciNetGoogle Scholar
  9. [9]
    H. Federer, Geometric measure theory, Springer-Verlag, 1969.Google Scholar
  10. [10]
    R. Fefferman, A theory of entropy in Fourier analysis, Adv. Math. 30 (1978), 171–201.CrossRefzbMATHMathSciNetGoogle Scholar
  11. [11]
    K. Hansson, Imbedding theorems of Sobolev type in potential theory, Math. Scand. 45 (1979), 77–102.zbMATHMathSciNetGoogle Scholar
  12. [12]
    V. Maz’ya, Sobolev spaces, Springer-Verlag, 1985.Google Scholar
  13. [13]
    V. Maz’ya, T. Shaposhinkova, Theory of multipliers in spaces of differentiable functions, Pitman Press, 1985.Google Scholar
  14. [14]
    N. Meyers, A theory of capacities for potentials of functions in Lebesgue classes, Math. Scand. 26 (1970), 255–292.zbMATHMathSciNetGoogle Scholar
  15. [15]
    N. Meyers, W. Ziemer, Integral inequalities of Poincaré and Wirtinger type for BV functions, Amer. J. Math, 99 (1977), 1345–1360.CrossRefzbMATHMathSciNetGoogle Scholar
  16. [16]
    C. Rogers, Hausdorff measures, Cambridge U. Press 1970.Google Scholar
  17. [17]
    F. Soria, Characterizations of classes of functions generated by blocks and associated Hardy spaces, Ind. U. Math. J. 34 (1985), 463–492.CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • David R. Adams
    • 1
  1. 1.Department of MathematicsUniversity of KentuckyLexingtonUSA

Personalised recommendations