Addendum to “Besov–Lipschitz and Mean Besov–Lipschitz Spaces”: The Ahern–Schneider Inequality

Abstract

Let f be a function holomorphic in the unit ball of \(\mathbb C^N\), and \(\mathcal Rf\) the radial derivative of f. It is proved that the Ahern–Schneider inequality \(\|\nabla f\|_{H^p}\le C_p\|\mathcal Rf\|_{H^p}\) holds for 0 < p < 1. This fills a gap in the proof of the main result in the paper “Besov–Lipschitz and mean Besov–Lipschitz spaces of holomorphic functions on the unit ball” [Potential Analysis] by Jevtic and Pavlovic.