Integral mean of Green’s potentials and their conjugate
The best possible estimates for Lebesgue integral means $m_q(r,F); (1le q <+infty)$ for the pair of functions $F= g+i:reve{g}$, here $g$ --- Green's potential, $reve{g}$ --- function conjugate to $g$, was obtained. It generalizes well-known results of Ya.V. Vasyl'kiv and A.A. Kondratyuk...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Vasyl Stefanyk Precarpathian National University
2013-06-01
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| Series: | Karpatsʹkì Matematičnì Publìkacìï |
| Subjects: | |
| Online Access: | http://journals.pu.if.ua/index.php/cmp/article/view/155/121 |
| Summary: | The best possible estimates for Lebesgue integral means $m_q(r,F); (1le q <+infty)$ for the pair of functions $F= g+i:reve{g}$, here $g$ --- Green's potential, $reve{g}$ --- function conjugate to $g$, was obtained. It generalizes well-known results of Ya.V. Vasyl'kiv and A.A. Kondratyuk for logarithms $log; B$ of Blaschke products $B$ in terms of counting function $n(r,0,B)$; $(0<r<1)$ of their zeroes. |
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| ISSN: | 2075-9827 |