Harmonic Hardy Spaces

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

Abstract

In Chapter 1 we defined the Poisson integral of a function f ∈ C(S) to be the function P[f] on B given by
(6.1)
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
(6.2)
Differentiating under the integral sign in 6.2, we see that P [μ] is har­monic on B.

Keywords

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