Some Spaces of Harmonic Functions in the Unit Ball of ℝn

Аннотация

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).