多重次调和函数的局部增长
复变函数
2009-12-03 v2
摘要
我们利用Siciak极值函数和相对极值函数得到了多重次调和函数局部增长的双界估计。作为应用，我们给出了“Bernstein加倍不等式”以及[Alexander Brudnyi, Local inequalities for pluri-subharmonic functions, Annals Math. 149 (1999), No. 2, pp. 511--533]中主要结果的简单新证明。我们提出了一个类似于[H. Alexander and B. A. Taylor, Comparison of two capacities in , Math. Z. 186 (1984), 407--417]中比较定理的猜想，该猜想的成立使得仅用Siciak极值函数即可得到多重次调和函数局部增长的界。
引用
@article{arxiv.0908.4355,
title = {Local growth of pluri-subharmonic functions},
author = {Tuyen Trung Truong},
journal= {arXiv preprint arXiv:0908.4355},
year = {2009}
}
备注
Complete arguments to new proofs of the main result in Brudnyi's paper and to the "Berstein doubling inequality" are added. Several other changes/corrections. 8 pages