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1980•Bulletin of the London Mathematical SocietyRequires access

Bloch Functions in Several Complex Variables, I

Richard M. Timoney

Open publisher page 235 citations

Abstract

Bloch functions on the unit disk are those analytic functions f for which the quantity |f′(z)|(1 − |z|2) is bounded (for z in the disk). In this paper, Bloch functions on bounded homogeneous domains in complex m-space are studied. The main result shows that many of the equivalent definitions of Bloch functions on the unit disk are also equivalent in the general setting.

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What this paper is about

Bloch functions on the unit disk are those analytic functions f for which the quantity |f′(z)|(1 − |z|2) is bounded (for z in the disk). In this paper, Bloch functions on bounded homogeneous domains in complex m-space are studied. The main result shows that many of the equivalent definitions of Bloch functions on the unit disk are also equivalent in the general setting.

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OpenAlex reports 235 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

Bloch functions on the unit disk are those analytic functions f for which the quantity |f′(z)|(1 − |z|2) is bounded (for z in the disk). In this paper, Bloch functions on bounded homogeneous domains in complex m-space are studied. The main result shows that many of the equivalent definitions of Bloch functions on the unit disk are also equivalent in the general setting.

Key concepts: Mathematics, Several complex variables, Pure mathematics, Holomorphic function

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