Harmonic Hardy Spaces

  • Sheldon Axler
  • Paul Bourdon
  • Wade Ramey
Part of the Graduate Texts in Mathematics book series (GTM, volume 137)


In Chapter 1 we defined the Poisson integral of a function f ∈ C(S) to be the function P[f] on B given by
We now extend this definition: for μ a complex Borel measure on S, the Poisson integral of μ, denoted μ[p], is the function on B defined by
Differentiating under the integral sign in 6.2, we see that P [μ] is har­monic on B.


Harmonic Function Normed Linear Space Borel Measurable Function Linear Isometry Nontangential Limit 
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Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Sheldon Axler
    • 1
  • Paul Bourdon
    • 2
  • Wade Ramey
    • 3
  1. 1.Mathematics DepartmentSan Francisco State UniversitySan FranciscoUSA
  2. 2.Mathematics DepartmentWashington and Lee UniversityLexingtonUSA
  3. 3.BerkeleyUSA

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