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Averaging properties
of pluriharmonic boundary values
Wade C. Ramey |
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Vol. 123 (1986), No. 2, 407–420
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Abstract |
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Suppose D ⊂ Cn is a smoothly bounded domain and u is bounded and pluriharmonic in D. Let u∗ denote the boundary function of u, and let ζ0 ∈ ∂D. It is shown that if u∗ has good averaging behavior on one curve in ∂D through ζ0, then u∗ has good averaging behavior on all curves in ∂D through ζ0, provided the curves in question satisfy a certain directional condition. These results fail if the directional condition on the curve is violated. |
Mathematical Subject Classification 2000
Primary: 32A40
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Milestones
Received: 8 February 1985
Revised: 25 September 1985
Published: 1 June 1986
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Authors |
| Wade C. Ramey | |
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