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Abstract
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Let
be the classical
domain of type
in
with
.
The purpose of this paper is twofold. The first is to investigate the boundary points
of
.
We give a sufficient and necessary condition such that the boundary points of
are
smooth. The second is to establish the boundary Schwarz lemma on the classical domain
of type
.
we obtain the optimal estimates of the eigenvalues of the Fréchet
derivative for holomorphic self-mappings at the smooth boundary point of
.
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Keywords
holomorphic mapping, Schwarz lemma at the boundary, the
classical domain of type $\mathcal{IV}$
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Mathematical Subject Classification 2010
Primary: 32H02
Secondary: 32H99, 30C80
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Milestones
Received: 2 May 2018
Revised: 13 August 2018
Accepted: 20 January 2019
Published: 5 November 2019
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