In this paper, Schwarz-Pick estimates for high order Fr′echet derivatives of bounded holomorphic functions on three kinds of classical domains are presented. We generalize the early work on Schwarz-Pick estimates of ...In this paper, Schwarz-Pick estimates for high order Fr′echet derivatives of bounded holomorphic functions on three kinds of classical domains are presented. We generalize the early work on Schwarz-Pick estimates of higher order partial derivatives for bounded holomorphic functions on the disk and unit ball.展开更多
In this paper we prove a Schwarz-Pick lemma for the modulus of holomorphic mappings from the polydisk into the unit ball. This result extends some related results.
Let f be a twice continuously differentiable self-mapping of a unit disk satisfying Poisson differential inequality |△f(z)| ≤ B · |Df(z)|^(2) for some B > 0 and f(0) = 0. In this note, we show that f does no...Let f be a twice continuously differentiable self-mapping of a unit disk satisfying Poisson differential inequality |△f(z)| ≤ B · |Df(z)|^(2) for some B > 0 and f(0) = 0. In this note, we show that f does not always satisfy the Schwarz-Pick type inequality (1-|z|^(2))/(1-|f(z)|^(2))≤ C(B),where C(B) is a constant depending only on B. Moreover, a more general Schwarz-Pick type inequality for mapping that satisfies general Poisson differential inequality is established under certain conditions.展开更多
In this article,we first establish an asymptotically sharp result on the higher order Fréchet derivatives for bounded holomorphic mappings f(x)=f(0)+∞∑s=1Dskf(0)(x^(sk))/(sk)!:B_(X)→B_(Y),where B_X is the unit...In this article,we first establish an asymptotically sharp result on the higher order Fréchet derivatives for bounded holomorphic mappings f(x)=f(0)+∞∑s=1Dskf(0)(x^(sk))/(sk)!:B_(X)→B_(Y),where B_X is the unit ball of X.We next give a sharp result on the first order Fréchet derivative for bounded holomorphic mappings F(X)=F(0+)∞∑s=KD^(s)f(0)(x^(8)/s!):B_(X)→B_(Y),where B_(X)is the unit ball of X.The results that we derive include some results in several complex variables,and extend the classical result in one complex variable to several complex variables.展开更多
We establish a precise Schwarz lemma for real-valued and bounded harmonic functions in the real unit ball of dimension n. This extends Chen's Schwarz-Pick lemma for real-valued and bounded planar harmonic mapping.
基金supported by National Natural Science Foundation of China (10871145 10926066)+1 种基金Doctoral Program Foundation of the Ministry of Education of China (20090072110053)Natural Science Foundation of Zhejiang Province (Y6100007)
文摘In this paper, Schwarz-Pick estimates for high order Fr′echet derivatives of bounded holomorphic functions on three kinds of classical domains are presented. We generalize the early work on Schwarz-Pick estimates of higher order partial derivatives for bounded holomorphic functions on the disk and unit ball.
基金supported by the National Natural Science Foundation of China(11201199)the Scientific Research Foundation of Jinling Institute of Technology(Jit-b-201221)Qing Lan Project
文摘In this paper we prove a Schwarz-Pick lemma for the modulus of holomorphic mappings from the polydisk into the unit ball. This result extends some related results.
基金supported by NNSF of China(11701111)NNSFs of Guangdong Province (2016A030310257 and 2015A030313346)the Visiting Scholar Program of Chern Institute of Mathematics at Nankai University when the authors worked as visiting scholars。
文摘Let f be a twice continuously differentiable self-mapping of a unit disk satisfying Poisson differential inequality |△f(z)| ≤ B · |Df(z)|^(2) for some B > 0 and f(0) = 0. In this note, we show that f does not always satisfy the Schwarz-Pick type inequality (1-|z|^(2))/(1-|f(z)|^(2))≤ C(B),where C(B) is a constant depending only on B. Moreover, a more general Schwarz-Pick type inequality for mapping that satisfies general Poisson differential inequality is established under certain conditions.
基金supported by the NSFC(11871257,12071130)supported by the NSFC(11971165)。
文摘In this article,we first establish an asymptotically sharp result on the higher order Fréchet derivatives for bounded holomorphic mappings f(x)=f(0)+∞∑s=1Dskf(0)(x^(sk))/(sk)!:B_(X)→B_(Y),where B_X is the unit ball of X.We next give a sharp result on the first order Fréchet derivative for bounded holomorphic mappings F(X)=F(0+)∞∑s=KD^(s)f(0)(x^(8)/s!):B_(X)→B_(Y),where B_(X)is the unit ball of X.The results that we derive include some results in several complex variables,and extend the classical result in one complex variable to several complex variables.
基金Research supported by the National Natural Science Foundation of China(1120119911071083+1 种基金11671361)Jiangsu Overseas Visiting Scholar Program for University Prominent Young&Middle-aged Teachers and Presidents
文摘We establish a precise Schwarz lemma for real-valued and bounded harmonic functions in the real unit ball of dimension n. This extends Chen's Schwarz-Pick lemma for real-valued and bounded planar harmonic mapping.
