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Proceedings of the Yerevan State University, series Physical and Mathematical Sciences, 2013, Issue 3, Pages 29–36
(Mi uzeru79)
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This article is cited in 3 scientific papers (total in 3 papers)
Mathematics
Duality in some spaces of functions harmonic in the unit ball
A. I. Petrosyan, E. S. Mkrtchyan Yerevan State University
Abstract:
We introduce the Banach spaces $h_{\infty}(\varphi), h_0(\varphi)$ and $h^1(\eta)$ of functions harmonic in the unit ball in $\mathbb{R}^ n $, depending on weight function $\varphi$ and weighting measure $\eta$. The paper studies the following question: for which $\varphi$ and $\eta$ we $h^1(\eta)^* \sim h_{\infty} (\eta)$ and $h_0(\varphi)^* \sim h^1 (\eta)$. We prove that the necessary and sufficient condition for this is that certain linear operator, which projects $L^{\infty}(d\eta\, d\sigma)$ onto the subspace $\varphi h_{\infty}(\varphi)$, is bounded.
Keywords:
Banach space, harmonic function, weight function, weighting measure, bounded projector.
Received: 11.04.2013 Accepted: 15.05.2013
Citation:
A. I. Petrosyan, E. S. Mkrtchyan, “Duality in some spaces of functions harmonic in the unit ball”, Proceedings of the YSU, Physical and Mathematical Sciences, 2013, no. 3, 29–36
Linking options:
https://www.mathnet.ru/eng/uzeru79 https://www.mathnet.ru/eng/uzeru/y2013/i3/p29
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Abstract page: | 99 | Full-text PDF : | 25 | References: | 47 |
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