A Schwarz Lemma at the Boundary of Hilbert Balls

作者：Chen, Zhihua; Liu, Yang^*; Pan, Yifei

来源：Chinese Annals of Mathematics Series B, 2018, 39(4): 695-704.

DOI：10.1007/s11401-018-0090-8

• Boundary Schwarz lemma
• Separable Hilbert space
• Holomorphic mapping
• Unit ball

In this paper, the authors prove a general Schwarz lemma at the boundary for the holomorphic mapping f between unit balls B and B' in separable complex Hilbert spaces H and H', respectively. It is found that if the mapping f is an element of C1+alpha at z(0) is an element of partial derivative B with f(z(0)) = w(0) is an element of partial derivative B', then the Frechet derivative operator Df(z(0)) maps the tangent space T-z0 (partial derivative B-n) to T-w0 (partial derivative B'), the holomorphic tangent space T-z0((1,0))(partial derivative B-n) to T-w0((1,0))(partial derivative B'), respectively.

• 出版日期2018-7
• 单位同济大学; 浙江师范大学