摘要
Bohr's type inequalities are studied in this paper: if f is a holomorphic mapping from the unit ball B^n to B^n, f(0)=p, then we have sum from k=0 to∞|Dφ_P(P)[D^kf(0)(z^k)]|／k!||Dφ_P(P)||＜1 for|z|＜max{1／2+|P|,(1-|p|)／2^(1／2)andφ_P∈Aut(B^n) such thatφ_(p)=0. As corollaries of the above estimate, we obtain some sharp Bohr's type modulus inequalities. In particular, when n=1 and |P|→1, then our theorem reduces to a classical result of Bohr.
Bohr＇s type inequalities are studied in this paper： if f is a holomorphic mapping from the
unit ball B^n to B^n, f（0）=p, then we have sum from k=0
to∞｜DφP（P）[D^kf（0）（z^k）]｜/k!｜｜DφP（P）｜｜〈1 for｜z｜〈max{1/2＋｜P｜,（1-｜p｜）/2^1/2andφ_P
∈Aut（B^n） such thatφ_（p）=0. As corollaries of the above estimate, we obtain some sharp Bohr＇s type
modulus inequalities. In particular, when n=1 and ｜P｜→1, then our theorem reduces to a classical
result of Bohr.
基金
Supported by the NNSF of China(10571164)
Supported by Specialized Research Fund for the Doctoral Program of Higher Education(SRFDP)(2050358052)
Supported by the NSF of Zhejiang Province(Y606197)
