WEIGHTED SPACES OF FUNCTIONS HARMONIC IN THE UNIT BALL

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Submitted: 2025-02-10; Published: 2025-02-10

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Abstract

We introduce the Banach spaces h∞(φ), h0(φ) and h1(ψ) functions harmonic in the unit ball B⊂Rn. These spaces depend on weight functions φ, ψ. We prove that if φ and ψ form a normal pair, then h1(ψ)∗∼h∞(φ) and h0(φ)∗∼h1(ψ).