Geodesic
Duality in some spaces of functions harmonic in the unit ball
Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 3 (2013), pp. 29-36

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{UZERU_2013_3_a4,
     author = {A. I. Petrosyan and E. S. Mkrtchyan},
     title = {Duality in some spaces of functions harmonic in the unit ball},
     journal = {Proceedings of the Yerevan State University. Physical and mathematical sciences},
     pages = {29--36},
     publisher = {mathdoc},
     number = {3},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UZERU_2013_3_a4/}
}
TY  - JOUR
AU  - A. I. Petrosyan
AU  - E. S. Mkrtchyan
TI  - Duality in some spaces of functions harmonic in the unit ball
JO  - Proceedings of the Yerevan State University. Physical and mathematical sciences
PY  - 2013
SP  - 29
EP  - 36
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/UZERU_2013_3_a4/
LA  - en
ID  - UZERU_2013_3_a4
ER  - 
%0 Journal Article
%A A. I. Petrosyan
%A E. S. Mkrtchyan
%T Duality in some spaces of functions harmonic in the unit ball
%J Proceedings of the Yerevan State University. Physical and mathematical sciences
%D 2013
%P 29-36
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/UZERU_2013_3_a4/
%G en
%F UZERU_2013_3_a4
A. I. Petrosyan; E. S. Mkrtchyan. Duality in some spaces of functions harmonic in the unit ball. Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 3 (2013), pp. 29-36. http://geodesic.mathdoc.fr/item/UZERU_2013_3_a4/