Bloch functions on the unit ball of an infinite dimensional Hilbert space

被引：38

作者：

Blasco, Oscar ^{[1
]}

Galindo, Pablo ^{[1
]}

Miralles, Alejandro ^{[2
]}

机构：

[1] Univ Valencia, Dept Anal Matemat, Valencia, Spain

[2] Univ Jaume I Castello UJI, Inst Univ Matemat & Aplicac Castellon IMAC, Castellon de La Plana, Spain

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2014年 / 267卷 / 04期

关键词：

Bloch function; Infinite dimensional holomorphy;

D O I：

10.1016/j.jfa.2014.04.018

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The Bloch space has been studied on the open unit disk of C and some homogeneous domains of C-n. We define Bloch functions on the open unit ball of a Hilbert space B and prove that the corresponding space B(B-E) is invariant under composition with the automorphisms of the ball, leading to a norm that - modulo the constant functions - is automorphism invariant as well. All bounded analytic functions on BE are also Bloch functions. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：1188 / 1204

页数：17

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