Boundary Behavior of Poisson Integrals

  • Walter Rudin
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 241)


The principal result of the present chapter is Korányi’s Theorem 5.4.5—the fact that certain maximal functions associated to invariant Poisson integrals are of weak type (1, 1). The existence of what we call “K-limits” at almost all points of S follows easily from this.


Positive Measure Maximal Function Complex Measure Weak Type Boundary Behavior 
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Copyright information

© Springer-Verlag New York Inc. 1980

Authors and Affiliations

  • Walter Rudin
    • 1
  1. 1.Department of MathematicsUniversity of WisconsinMadisonUSA

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