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.
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
\Bibitem{Hay21}
\by F.~V.~Hayrapetyan
\paper On weighted solutions of $\overline{\partial}$-equation in the unit disc
\jour Proceedings of the YSU, Physical and Mathematical Sciences
\yr 2021
\vol 55
\issue 1
\pages 20--28
\mathnet{http://mi.mathnet.ru/uzeru828}
\crossref{https://doi.org/10.46991/PYSU:A/2021.55.1.020}
Linking options:
https://www.mathnet.ru/eng/uzeru828
https://www.mathnet.ru/eng/uzeru/v55/i1/p20
This publication is cited in the following 1 articles:
F. V. Hayrapetyan, A. H. Karapetyan, A. A. Karapetyan, “On Weighted Solutions to $\overline{{\partial}}$-Equation in the Upper Half-Plane”, J. Contemp. Mathemat. Anal., 56:5 (2021), 270
Citation in format AMSBIB
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