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1978•Proceedings of the American Mathematical SocietyRequires access

Two theorems on boundary values of analytic functions

S. R. Barker

Open publisher page 11 citations

Abstract

We give a new admissible maximal inequality for analytic functions of several complex variables, and also show that an analytic function which is admissibly bounded at almost all boundary points of a domain D must have an admissible limit a.e. These results are then applied to the boundary behaviour of the Nevanlinna class of D .

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What this paper is about

We give a new admissible maximal inequality for analytic functions of several complex variables, and also show that an analytic function which is admissibly bounded at almost all boundary points of a domain D must have an admissible limit a.e. These results are then applied to the boundary behaviour of the Nevanlinna class of D .

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OpenAlex reports 11 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

We give a new admissible maximal inequality for analytic functions of several complex variables, and also show that an analytic function which is admissibly bounded at almost all boundary points of a domain D must have an admissible limit a.e. These results are then applied to the boundary behaviour of the Nevanlinna class of D .

Key concepts: Analytic function, Mathematics, Bounded function, Quasi-analytic function, Boundary (topology), Class (philosophy), Domain (mathematical analysis), Boundary values

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