Bounded solutions for \(\bar \partial\)-problem in pseudo-Siegel domains
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.
scientific article; zbMATH DE number 878444