DUALITY IN SOME SPACES OF FUNCTIONS HARMONIC IN THE UNIT BALL

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Submitted: 2025-02-17; Published: 2025-02-17

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Abstract

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.