Volume densities with the mean value property for harmonic functions
Volume densities with the mean value property for harmonic functions
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具有调和函数平均值属性的体积密度
DOI：
10.1090/s0002-9939-1995-1213859-3
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发表时间：
1995
期刊：
影响因子：
--
通讯作者：
I. Netuka
中科院分区：
文献类型：
--
作者：
W. Hansen;I. Netuka
在包含原点的Rd有界域U上，研究了U上每一个有界调和函数相对于Lebesgue测度密度为w且满足h(O) = f h du的概率测度U。对于任意这样的度量，构造一个域U使inf (U) = 0。（这解决了a. Cornea提出的一个问题。）然而，如果U有光滑的边界，那么U的密度是w E F？在U上离0有界的(U)可以构造。另一方面，对于任意U，总有可能选择一个严格正的w E F？(U)在U点趋于零。
On a bounded domain U in Rd containing the origin, probability measures u which have a density w with respect to Lebesgue measure and satisfy h(O) = f h du for every bounded harmonic function on U are studied. A domain U is constructed such that inf w (U) = 0 for any such measure. (This solves a problem proposed by A. Cornea.) If, however, U has smooth boundary, then u having a density w E F? (U) which is bounded away from zero on U can be constructed. On the other hand, for arbitrary U it is always possible to choose a strictly positive w E F? (U) tending to zero at a U.