WEIGHTED SPACES OF FUNCTIONS HARMONIC IN THE UNIT BALL - Petrosyan, A.I.; Avetisyan, K.I. (Proceedings of the YSU A: Physical and Mathematical Sciences, 2017)
We introduce the Banach spaces $h_{∞}(φ)$, $h_{0}(φ)$ and $h^{1}(ψ)$ functions harmonic in the unit ball $B\subset\mathbb{R}^n$. These spaces depend on weight functions $φ$, $ψ$. We prove that if $φ$ and $ψ$ form a normal pair, then $h^{1}(ψ)^*\sim h_{∞}(φ)$ and $h_{0}(φ)^*\sim h^{1}(ψ)$.
Keywords: Banach space, harmonic function, weight function, duality