Volume densities with the mean value property for harmonic functions

Hansen W, Netuka I (1995)
Proceedings of the American Mathematical Society 123(1): 135-140.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
On a bounded domain U in R(d) containing the origin, probability measures mu which have a density w with respect to Lebesgue measure and satisfy h(0) = integral h d mu 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 mu having a density w is an element of C infinity (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 is an element of C infinity (U) tending to zero at partial derivative U.
Stichworte
MEAN VALUE PROPERTY; HARMONIC FUNCTIONS; BALAYAGE MEASURES
Erscheinungsjahr
1995
Zeitschriftentitel
Proceedings of the American Mathematical Society
Band
123
Ausgabe
1
Seite(n)
135-140
ISSN
0002-9939
Page URI
https://pub.uni-bielefeld.de/record/1641777

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Hansen W, Netuka I. Volume densities with the mean value property for harmonic functions. Proceedings of the American Mathematical Society . 1995;123(1):135-140.
Hansen, W., & Netuka, I. (1995). Volume densities with the mean value property for harmonic functions. Proceedings of the American Mathematical Society , 123(1), 135-140. doi:10.2307/2160618
Hansen, W., and Netuka, I. (1995). Volume densities with the mean value property for harmonic functions. Proceedings of the American Mathematical Society 123, 135-140.
Hansen, W., & Netuka, I., 1995. Volume densities with the mean value property for harmonic functions. Proceedings of the American Mathematical Society , 123(1), p 135-140.
W. Hansen and I. Netuka, “Volume densities with the mean value property for harmonic functions”, Proceedings of the American Mathematical Society , vol. 123, 1995, pp. 135-140.
Hansen, W., Netuka, I.: Volume densities with the mean value property for harmonic functions. Proceedings of the American Mathematical Society . 123, 135-140 (1995).
Hansen, Wolfhard, and Netuka, I. “Volume densities with the mean value property for harmonic functions”. Proceedings of the American Mathematical Society 123.1 (1995): 135-140.