Global analyticity of the canonical solution of \(\bar\partial_b\) for a class of pseudoconvex compact hypersurfaces of \(\mathbb{C}^2\) (Q1378335)

This paper deals with a class of pseudoconvex compact hypersurfaces in \(\mathbb{C}^2\) for which the canonical solution of the \(\overline\partial_b\) Neumann problem turns out to be globally analytic. The author considers the hypersurface \(S= \partial\Omega\), \(\Omega= \{| w|^2+ \rho(z,\overline z)< 0\}\subset \mathbb{C}^2_{w,z}\), where \(\rho\in C^\omega(\mathbb{C})\), and \(\Omega\) is a bounded and regular domain. According to the main result of this paper, if \(u\) is a canonical solution of the equation \(\overline\partial_b u=f\) on \(S\) and if \(f\in C^\omega(S)\) then \(u\in C^\omega(S)\).