DUALITY IN SOME SPACES OF FUNCTIONS HARMONIC IN THE UNIT BALL

Authors

  • A.I. Petrosyan Chair of General Mathematics, YSU, Armenia
  • E.S. Mkrtchyan Chair of General Mathematics, YSU, Armenia

DOI:

https://doi.org/10.46991/PYSU:A/2013.47.3.029

Keywords:

Banach space, harmonic function, weight function, weighting measure, bounded projector

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 have $h^{1}(\eta)^*\sim h_{\infty}(\eta)$ 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.

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Published

2013-11-20

How to Cite

Petrosyan, A., & Mkrtchyan, E. (2013). DUALITY IN SOME SPACES OF FUNCTIONS HARMONIC IN THE UNIT BALL. Proceedings of the YSU A: Physical and Mathematical Sciences, 47(3 (232), 29–36. https://doi.org/10.46991/PYSU:A/2013.47.3.029

Issue

Section

Mathematics