| Title | Jensen measures, hyperconvexity and boundary behaviour of the pluricomplex Green function |
| Authors | Magnus Carlehed, Urban Cegrell, Frank Wikström |
| Publication | ANNALES POLONICI MATHEMATICI |
| Year | 1999 |
| Volume | 71 |
| Issue | 1 |
| Pages | 87 - 103 |
| Document type | Article |
| Status | Published |
| Quality controlled | Yes |
| Language | eng |
| Abstract English | Let <br> be a bounded domain in CN. Let z be a point in <br> and let Jz be the set of all Jensen<br> measures on <br> with barycenter at z with respect to the space of functions continuous on <br> and<br> plurisubharmonic in <br> . The authors prove that <br> is hyperconvex if and only if, for every z 2 @<br> ,<br> measures in Jz are supported by @<br> . From this they deduce that a pluricomplex Green function<br> g(z,w) with its pole at w continuously extends to @<br> with zero boundary values if and only if <br> <br> is hyperconvex.<br> Then the authors give a criterion for Reinhardt domains to be hyperconvex and explicitly compute<br> the pluricomplex Green function on the Hartogs triangle.<br> The last sections are devoted to the boundary behaviour of pluricomplex Green functions. Such<br> a function has Property (P0) at a point w0 2 @<br> if limw!w0 g(z,w) = 0 for every z 2 <br> . If the<br> convergence is uniform in z on compact subsets of <br> r{w0}, then w0 has Property (P0). Several<br> sufficient conditions for points on the boundary with these properties are given. |
| ISBN/ISSN/Other | ISSN: 1730-6272(e) |
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