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1986•Complex Variables Theory and Application An International JournalRequires access

Cauchy and poisson integral representations of generalizations of Hp functions

R. D. Carmichael

Open publisher page 3 citations

Abstract

Holomorphic functions in tubes which generalize the Hardy Hp functions are considered. In previous work the existence of strong l′ distributional boundary values for the holomorphic functions has been established. In this paper we show that if these boundary values are in the distribution space then the holomorphic functions can be recovered by the Cauchy and Poisson integrals of the boundary values.

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Holomorphic functions in tubes which generalize the Hardy Hp functions are considered. In previous work the existence of strong l′ distributional boundary values for the holomorphic functions has been established. In this paper we show that if these boundary values are in the distribution space then the holomorphic functions can be recovered by the Cauchy and Poisson integrals of the boundary values.

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Available abstract

Holomorphic functions in tubes which generalize the Hardy Hp functions are considered. In previous work the existence of strong l′ distributional boundary values for the holomorphic functions has been established. In this paper we show that if these boundary values are in the distribution space then the holomorphic functions can be recovered by the Cauchy and Poisson integrals of the boundary values.

Key concepts: Holomorphic function, Mathematics, Cauchy distribution, Cauchy's integral formula, Poisson distribution, Boundary (topology), Mathematical analysis, Boundary values

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