ON WEIGHTED SOLUTIONS OF $\overline{\partial}$-EQUATION IN THE UNIT DISC
2021 ◽
Vol 55
(1 (254))
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pp. 20-28
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).
2002 ◽
Vol 57
(4)
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pp. 6
2019 ◽
Vol 11
(01)
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pp. 1950006
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1999 ◽
Vol 38
(2)
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pp. 119-136
2021 ◽
Vol 240
(2)
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pp. 809-875