Bloch functions on bounded symmetric domains

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• 作者：Cho-Ho Chu^a ; ^{c.chu@qmul.ac.uk} ; Hidetaka Hamada^b ; ^{h.hamada@ip.kyusan-u.ac.jp} ; Tatsuhiro Honda^c ; ^{thonda@cc.it-hiroshima.ac.jp} ; Gabriela Kohr^d ; ^{gkohr@math.ubbcluj.ro}
• 关键词：32A18 ; 32A30 ; 46L70
• 刊名：Journal of Functional Analysis
• 出版年：2017
• 出版时间：15 March 2017
• 年：2017
• 卷：272
• 期：6
• 页码：2412-2441
• 全文大小：515 K
• 卷排序：272

文摘

We introduce and characterize Bloch functions on bounded symmetric domains, which may be infinite dimensional, by extending several well-known equivalent conditions for Bloch functions on the open unit disc U   in CC. We also generalize a number of results concerning Bloch functions on U to bounded symmetric domains. Given a holomorphic mapping φ   between bounded symmetric domains BXBX and BYBY, we derive criteria for boundedness and compactness of the composition operator CφCφ between the Bloch spaces B(BY)B(BY) and B(BX)B(BX), extending several known results for finite dimensional domains.