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This article is cited in 1 scientific paper (total in 1 paper)
Mathematics
On weighted solutions of $\overline{\partial}$-equation in the unit disc
F. V. Hayrapetyan Yerevan State University, Faculty of Mathematics and Mechanics
Abstract:
In the paper an equation $\partial g(z)/\partial \overline{z} = v(z)$ is considered in the unit disc $\mathbb{D}$. For $C^k$-functions $v$ $(k = 1,2,3,\dots, \infty)$ from weighted $L^p$-classes $(1 \leq p < \infty)$ with weight functions of the type $|z|^{2\gamma} (1-|z|^{2\rho})^{\alpha}$, $z \in \mathbb{D}$, a family $g_{\beta}$ of solutions is constructed ($\beta$ is a complex parameter).
Keywords:
$\overline{\partial}$-equation, weighted function spaces.
Received: 09.03.2021 Revised: 30.03.2021 Accepted: 06.04.2021
Citation:
F. V. Hayrapetyan, “On weighted solutions of $\overline{\partial}$-equation in the unit disc”, Proceedings of the YSU, Physical and Mathematical Sciences, 55:1 (2021), 20–28
Linking options:
https://www.mathnet.ru/eng/uzeru828 https://www.mathnet.ru/eng/uzeru/v55/i1/p20
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Abstract page: | 85 | Full-text PDF : | 26 | References: | 8 |
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