摘要
Let R_I(m,n) be the classical domain of type I in C^(m×n)with 1≤m≤n.We obtain the optimal estimates of the eigenvalues of the Fréchet derivative Df(Z) at a smooth boundary fixed point Z of R_I(m,n)for a holomorphic self-mapping f of R_L(m,n).We provide a necessary and sufficient condition such that the boundary points of R_I(m,n) are smooth,and give some properties of the smooth boundary points of R_L(m,n).Our results extend the classical Schwarz lemma at the boundary of the unit disk △ to R_I(m,n),which may be applied to get some optimal estimates in several complex variables.
Let RI（m,n） be the classical domain of type I in C^m×n with 1≤m≤n.We obtain the optimal estimates of the eigenvalues of the Fréchet derivative Df（Z） at a smooth boundary fixed point Z of RI（m,n）for a holomorphic self-mapping f of RL（m,n）.We provide a necessary and sufficient condition such that the boundary points of RI（m,n） are smooth,and give some properties of the smooth boundary points of RL（m,n）.Our results extend the classical Schwarz lemma at the boundary of the unit disk △ to RI（m,n）,which may be applied to get some optimal estimates in several complex variables.
基金
National Natural Science Foundation of China(Grant Nos. 11571105 and 11471111)
Natural Science Foundation of Zhejiang Province(Grant No.LY14A010017)
