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2000•Complex Variables Theory and Application An International JournalRequires access

On quaternionic bergman and poly-bergman spaces

Nikolai Vasilevski

Open publisher page 7 citations

Abstract

Let п be the upper half-space in consider the Bergman space , the subspace of all left-ψ-hyper-holomorphic valued functions from . Complete decomposition of onto Bergman and Bergman type spaces of poly-ψ-hyper-holomorphic and poly-ψ-hyper-holomorphic functions is obtained. Simple isomorphic descriptions of all these spaces are given. Connections with the Hardy spaces and the Szegö projections are established.

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What this paper is about

Let п be the upper half-space in consider the Bergman space , the subspace of all left-ψ-hyper-holomorphic valued functions from . Complete decomposition of onto Bergman and Bergman type spaces of poly-ψ-hyper-holomorphic and poly-ψ-hyper-holomorphic functions is obtained. Simple isomorphic descriptions of all these spaces are given. Connections with the Hardy spaces and the Szegö projections are established.

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Available abstract

Let п be the upper half-space in consider the Bergman space , the subspace of all left-ψ-hyper-holomorphic valued functions from . Complete decomposition of onto Bergman and Bergman type spaces of poly-ψ-hyper-holomorphic and poly-ψ-hyper-holomorphic functions is obtained. Simple isomorphic descriptions of all these spaces are given. Connections with the Hardy spaces and the Szegö projections are established.

Key concepts: Bergman kernel, Bergman space, Mathematics, Pure mathematics, Mathematical analysis, Bounded function

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