引入第一类典型域RI(m,n)上的全纯映照子族Hk(RI(m,n)),当k→ +∞时,该映照族就是RI(m,n)上的局部双全纯映照族.建立了Hk(RI(m,n))上的Bonk偏差定理.当k=1和k→ +∞时,其结果分别都回到了FitzGerad和龚升关于典型域RI(m,n)上的Bonk偏差定理.当m=n=1时, 其结果又回到了Liu和Minda在单位圆盘上的偏差定理.应用偏差定理,给出了映照族Hk(RI(m,n))上的Bloch常数估计,其结果补全了从k=1和k→ +∞之间的RI(m,n)上Bloch常数估计的所有结果,而且把单位球上的Bloch常数估计推广到RI(m,n)上.
Abstract
In this paper, various subfamilies Hk(RI(m,n))of holomorphic mappings defined in the first classical domain RI(m,n)are introduced. When k tends to +∞, this family reduces to the class of locally biholomorphic mappings on RI(m,n). We establish the Bonk distortion theorems for Hk(RI(m,n)). In particular, when k = 1 and k → +∞, the theorems reduce to that of Fitzgerald and Gong, respectively. When m = n = 1, this distortion theorem coincides with Liu and Minda as the unit disk case. As applications of the Bonk distortion theorems, various estimates of Bloch constants for these subfamilies of holomorphic mappings on RI(m,n)are obtained. We not only give all Bloch estimates of holomorphic mappings between 1 < k < +∞ defined in RI(m,n), but also extend our early Bloch constant estimates of the unit ball to the classical domain of the first type RI(m,n).
关键词
典型域 /
全纯映照 /
偏差定理 /
Bloch常数
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Key words
classical domain /
holomorphic mapping /
distortion theorem /
Bloch constant
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参考文献
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脚注
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基金
国家自然科学基金资助项目(10826083, 10971063, 11001246); 浙江省自然科学基金(D7080080, Y6090694, Y6110260, Y6110053); 浙江省创新团队资助项目(T200924, T200905)
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