3G-inequality for planar domains

Hansen W (2012)
Probability Theory and Related Fields 152(1-2): 357-366.

Zeitschriftenaufsatz | Veröffentlicht| Englisch
 
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Abstract / Bemerkung
The 3G-inequality for Green functions g(D) on arbitrary bounded domains in R-2, which Bass and Burdzy (Probab Theory Relat Fields 101(4): 479- 493, 1995) obtained by a genuinely probabilistic proof (using loops of Brownian motion around the origin), is proven (in a more precise form) employing elementary properties of harmonic measures only. Since harmonic measures are hitting distributions of Brownian motion, this purely analytic proof can be viewed as well as being probabilistic. A spin- off is an upper estimate of gD on subdisks B' of an open disk B in terms of gB divided by the capacity of B' \ D with respect to B.
Stichworte
Planar domain; Green function; Capacity; Harmonic measure; Brownian; motion; Loop; Greenian domain; 3G-inequality
Erscheinungsjahr
2012
Zeitschriftentitel
Probability Theory and Related Fields
Band
152
Ausgabe
1-2
Seite(n)
357-366
ISSN
0178-8051
Page URI
https://pub.uni-bielefeld.de/record/2474312

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Hansen W. 3G-inequality for planar domains. Probability Theory and Related Fields. 2012;152(1-2):357-366.
Hansen, W. (2012). 3G-inequality for planar domains. Probability Theory and Related Fields, 152(1-2), 357-366. doi:10.1007/s00440-010-0335-2
Hansen, W. (2012). 3G-inequality for planar domains. Probability Theory and Related Fields 152, 357-366.
Hansen, W., 2012. 3G-inequality for planar domains. Probability Theory and Related Fields, 152(1-2), p 357-366.
W. Hansen, “3G-inequality for planar domains”, Probability Theory and Related Fields, vol. 152, 2012, pp. 357-366.
Hansen, W.: 3G-inequality for planar domains. Probability Theory and Related Fields. 152, 357-366 (2012).
Hansen, Wolfhard. “3G-inequality for planar domains”. Probability Theory and Related Fields 152.1-2 (2012): 357-366.