| [1] 林运泳, 洪毅. Banach空间中全纯映射的若干性质. 数学学报, 1995, 38:234-241 Lin Y Y, Hong Y. Some properties of holomorphic maps in Banach spaces (in Chinese). Acta Math Sinica, 1995, 38:234-241
[2] Pavlovc M. A Schwarz lemma for the modulus of a vector-valued analytic functions. Proc Amer Math Soc, 2011, 139(3):969-973
[3] Ruscheweyh S. Two remarks on bounded analytic functions. Serdica, 1985, 11:200-202
[4] Dai S Y, Pan Y F. A Schwarz-Pick lemma for the modulus of holomorphic mappings from the polydisk into the unit ball. Acta Math Sci, 2014, 34B(6):1775-1780
[5] Avkhadiev F G, Wirths K J. Schwarz-Pick inequalities for derivatives of arbitrary order. Constr Approx, 2003, 19:265-277
[6] Dai S Y, Pan Y F. Note on Schwarz-Pick estimates for bounded and positive real part analytic functions. Proc Amer Math Soc, 2008, 136:635-640
[7] Liu Y, Chen Z H. Schwarz-pick estimates for holomorphic mappings from the polydisk to the unit ball. J Math Anal Appl, 2011, 376:123-128
[8] Liu Y, Chen Z H. Schwarz-Pick estimates for positive real part holomorphic functions on unit ball and polydisc. Science in China, 2010, 53(4):1017-1024
[9] Liu Y, Chen Z H. Schwarz-Pick estimates for bounded holomorphc functions on class domains. Acta Math Sci, 2011, 31B(4):1377-1382
[10] Dai S Y, Chen H H. Schwarz-Pick estimates for partial derivatives of arbitary order of bounded holomorphic functions in the unit ball of Cn. Acta Math Sci, 2011, 31B(4):1624-1632
[11] Dai S Y, Chen H J, Pan Y F. The Schwarz-Pick lemma of high order in several variables. Michigan Math J, 2010, 59:517-533
[12] Liu Y, Dai S Y. A note on Schwarz lemma for the modulus of holomorphic mappings on D. Acta Math Sci, 2015, 35B(1):89-94
[13] Graham I, Kohr G. Geometric Function Theory in One and Higher Dimensions. New York:Marcel Dekker, 2003 |
.jpg){kind=small}
|zi|p<1}，1 < p < +∞.该文证明了若f∈Hm（D，Bp），则|▽||f||（z）|≤（m|z|m-1）/（1-|z|2m）（1-||f（z）||2），z∈D.同时，当p为偶数时，该文也讨论了相应的极值问题，所得结论推广了一些相关结果.