Acta mathematica scientia, Series B >
A NOTE ON SCHWARZ LEMMA FOR THE MODULUS OF HOLOMORPHIC MAPPINGS ON D
Received date: 2014-01-24
Online published: 2015-01-20
Supported by
This work was supported by National Natural Science Foundations of China (11011373, 11201199, 11271333) and Zhejiang Provincial Natural Science Foundation of China (LY14A010008).
In this note, we consider a holomorphic mapping f from the unit disk D in C to p-ball Bp = z ∈ Cn :
n Pi=1 |zi|p < 1 , 1 < p < +∞. It is proved that for such f, |∇||f||(z)| ≤ 1 − ||f(z)||2 1 − |z|2 , z ∈ D. The extremal problem is also discussed when p is an even number. This result extends some related results on Schwarz lemma.
Key words： Schwarz lemma; holomorphic mapping; p-ball
LIU Yang, DAI ShaoYu . A NOTE ON SCHWARZ LEMMA FOR THE MODULUS OF HOLOMORPHIC MAPPINGS ON D[J]. Acta mathematica scientia, Series B, 2015 , 35(1) : 89 -94 . DOI: 10.1016/S0252-9602(14)60141-7
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