WEIGHTED SPACES OF FUNCTIONS HARMONIC IN THE UNIT BALL

Authors

  • A.I. Petrosyan Chair of General Mathematics, YSU, Armenia
  • K.I. Avetisyan Chair of General Mathematics, YSU, Armenia

DOI:

https://doi.org/10.46991/PYSU:A/2017.51.1.003

Keywords:

Banach space, harmonic function, weight function, duality

Abstract

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

Issue

Section

Mathematics