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
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.
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© 2001 Springer Science+Business Media New York
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Axler, S., Bourdon, P., Ramey, W. (2001). Harmonic Hardy Spaces. In: Harmonic Function Theory. Graduate Texts in Mathematics, vol 137. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-8137-3_6
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DOI: https://doi.org/10.1007/978-1-4757-8137-3_6
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-2911-2
Online ISBN: 978-1-4757-8137-3
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