DUALITY IN SPACES OF FUNCTIONS PLURIHARMONIC IN THE UNIT BALL IN $\mathbb{C}^n$
DOI:
https://doi.org/10.46991/PSYU:A/2016.50.2.015Keywords:
pluriharmonic function, unit ball in $\mathbb{C}^n$, duality, weighted spaces, projection, reproducing kernelAbstract
Banach spaces $h_\infty (\varPhi)$, $h_0 (\varPhi)$ and $h^1(\eta) $ of functions, pluriharmonic in the unit ball in $\mathbb{C}^n$, depending on weight function $\varPhi$ and weighting measure $\eta$ are introduced. The question we consider is: for given $\varPhi$ we find a finite positive Borel measure $\eta$ on $[0,1)$ such that $h^1(\eta)^* $ $\thicksim$ $h_\infty (\varPhi)$ and $h_0 (\varPhi)^*$ $\thicksim$ $h^1(\eta) $.
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2016-06-06
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Mathematics
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DUALITY IN SPACES OF FUNCTIONS PLURIHARMONIC IN THE UNIT BALL IN $\mathbb{C}^n$. (2016). Proceedings of the YSU A: Physical and Mathematical Sciences, 50(2 (240), 15-21. https://doi.org/10.46991/PSYU:A/2016.50.2.015