DUALITY IN SOME SPACES OF FUNCTIONS HARMONIC IN THE UNIT BALL

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DUALITY IN SOME SPACES OF FUNCTIONS HARMONIC IN THE UNIT BALL A. Petrosyan

We introduce the Banach spaces h∞(φ), h0(φ) and h1(η) of functions harmonic in the unit ball in Rn, depending on weight function φ and weighting measure η. The paper studies the following question: for which φ and η we have h1(η)∗∼h∞(η) and h0(φ)∗∼h1(η). We prove that the necessary and sufficient condition for this is that certain linear operator, which projects L∞(dηdσ) onto the subspace φh∞(φ), is bounded.

DOI: 10.46991/PYSUA.2013.47.3.029 Physical and Mathematical Sciences, 47(3 (232) 29-36

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Keywords

Banach space, harmonic function, weight function, weighting measure, bounded projector

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