Bounded solutions for \(\bar \partial\)-problem in pseudo-Siegel domains
type: Item
instance of: scholarly article
title: Bounded solutions for \(\bar \partial\)-problem in pseudo-Siegel domains
zbMATH Open document ID: 0851.35097
DOI: 10.1007/BF01759256
author: Elisabetta Barletta
author: Carla Parrini
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 1996-11-18T00:00:00Z
review text: Let \(S_p= \{z= (z_1,\dots, z_n)\in \mathbb{C}^n: \rho(z)= \sum^{n- 1}_{k= 1} |z_k|^{2p_k}+ \text{Im } z^{p_n}_n- 1< 0\}\) be the generalization of the classical Siegel domain \[ S= \Biggl\{ z\in \mathbb{C}^n: \rho(z)= \sum^{n- 1}_{k= 1} |z_k|^2+ \text{Im } z_n- 1\Biggr\}. \] The authors investigate the existence of bounded solutions to the inhomogeneous Cauchy-Riemann equations \(\overline\partial u= f\) with \(C^\infty\)-closed \((0, 1)\)-form \(f\) satisfying the condition \(|z|^k |k|< \infty\) at infinity.
Mathematics Subject Classification ID: 35N15
Mathematics Subject Classification ID: 32A07
zbMATH DE Number: 878444
zbMATH Keywords: Siegel domain
zbMATH Keywords: Cauchy-Riemann equations
reviewed by: Abduhamid Džuraev
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 878444