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
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© Springer Science+Business Media New York 2001