Harmonic Hardy Spaces
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 byWe 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 byDifferentiating under the integral sign in 6.2, we see that P [μ] is harmonic on B.
KeywordsHarmonic 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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© Springer Science+Business Media New York 2001