WEIGHTED SPACES OF FUNCTIONS HARMONIC IN THE UNIT BALL
DOI:
https://doi.org/10.46991/PYSU:A/2017.51.1.003Keywords:
Banach space, harmonic function, weight function, dualityAbstract
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 $h_{0}(\varphi)^*\sim h^{1}(\psi)$.
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Published
2017-03-20
How to Cite
Petrosyan, A., & Avetisyan, K. (2017). WEIGHTED SPACES OF FUNCTIONS HARMONIC IN THE UNIT BALL. Proceedings of the YSU A: Physical and Mathematical Sciences, 51(1 (242), 3–7. https://doi.org/10.46991/PYSU:A/2017.51.1.003
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Mathematics
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Copyright (c) 2017 Proceedings of the YSU
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