An Invariant Volume-Mean-Value Property

If ƒ is harmonic and integrable over the open unit disc U then so is ƒ ∘ ψ for every Moebius transformation ψ of U, and therefore 1 π ∫ U (ƒ ∘ ψ) d A = ƒ(ψ(0) for every ψ. Conversely, does this mean-value property imply that ƒ is harmonic? A more general question, with the unit ball B n of C (for ar...

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Veröffentlicht in:	Journal of functional analysis 1993-02, Vol.111 (2), p.380-397
Hauptverfasser:	Ahern, P., Flores, M., Rudin, W.
Format:	Artikel
Sprache:	eng
Schlagworte:	Exact sciences and technology Mathematical analysis Mathematics Potential theory Sciences and techniques of general use
Online-Zugang:	Volltext
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