Some Spaces of Harmonic Functions in the Unit Ball of ℝn

We introduce the Banach spaces h ∞ ( ϕ ) , h 0 ( ϕ ) and h 1 ( ψ ) functions harmonic in the unit ball B ⊂ ℝ n . These spaces depend on weight functions ϕ, ψ . We prove that if ϕ and ψ form a normal pair, then h 1 ( ψ ) * ∼ h ∞ ( ϕ ) and h 0 ( ϕ )* ∼ h 1 ( ψ ).

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Bibliographic Details
Published in:Lobachevskii journal of mathematics 2019-08, Vol.40 (8), p.1132-1136
Main Author: Petrosyan, A. I.
Format: Article
Language:English
Subjects:
Algebra
Analysis
Geometry
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Probability Theory and Stochastic Processes
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Summary:We introduce the Banach spaces h ∞ ( ϕ ) , h 0 ( ϕ ) and h 1 ( ψ ) functions harmonic in the unit ball B ⊂ ℝ n . These spaces depend on weight functions ϕ, ψ . We prove that if ϕ and ψ form a normal pair, then h 1 ( ψ ) * ∼ h ∞ ( ϕ ) and h 0 ( ϕ )* ∼ h 1 ( ψ ).
ISSN:1995-0802
1818-9962
DOI:10.1134/S1995080219080213