On a family of weighted  $\overline\partial$-integral representations in the unit disc

Feliks Hayrapetyan

doi:10.52737/18291163-2020.12.11-1-16

Authors

Feliks Hayrapetyan Institute of Mathematics, National Academy of Sciences of the Republic of Armenia

DOI:

https://doi.org/10.52737/18291163-2020.12.11-1-16

Keywords:

Smooth Functions in the Unit Disc, Weighted Function Spaces, Weighted $\overline{\partial}$-Integral Representations

Abstract

For weighted $L^p$-classess of $C^1$-functions in the unit disc with weight function of the type $|w|^{2\gamma}\cdot(1-|w|^{2\rho})^{\alpha}$, we obtain a family of weighted $\overline{\partial}$-integral representations of the type $f = P(f) - T(\overline{\partial} f)$.

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