Geodesic
Weighted spaces of functions harmonic in the unit ball
Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 51 (2017) no. 1, pp. 3-7

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We introduce the Banach spaces $h_{\infty}(\varphi)$, $h_{0}(\varphi)$ and $h^{1}(\psi)$ functions harmonic in the unit ball $B\subset\mathbb{R}^n$. These spaces depend on weight functions $\varphi$, $\psi$. We prove that if $\varphi$ and $\psi$ form a normal pair, then $h^{1}(\psi)^*\sim h_{\infty}(\varphi)$ and $h_{0}(\varphi)^*\sim h^{1}(\psi)$.
Keywords: Banach space, harmonic function, weight function, duality. 
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A. I. Petrosyan; K. L. Avetisyan. Weighted spaces of functions harmonic in the unit ball. Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 51 (2017) no. 1, pp. 3-7. http://geodesic.mathdoc.fr/item/UZERU_2017_51_1_a0/