Carleson measure characterizations of BMOA on pseudoconvex domains (Q1365143)

The authors prove the complex version of a theorem of \textit{C. Fefferman} and \textit{E. M. Stein} [Acta Math. 129, 137-193 (1972; Zbl 0257.46078)] on the Carleson measure characterization of BMOA. The domain treated here is defined by \(\Omega=\{z\in{\mathcal C}^n:r(z)>0\}\), where \(r\) is a smooth real-valued function such that \(|\Delta r|=1\) on \(\partial\Omega\) and assumed that \(\Omega\) is a pseudo-convex domain in \({\mathcal C}^2\) or a strongly pseudo-convex domain in \({\mathcal C}^n\) for \(n>2\). Several equivalent conditions in Carleman measure for \(f\in BMOA(\Omega)\) are given.