Essential norm of composition operators on the Hardy space H 1 and the weighted Bergman spaces $${A_{\alpha}^{p}}$$ on the ball

Abstract

We estimate the essential norm of a composition operator acting on the Hardy space H1 and the weighted Bergman spaces \({A_{\alpha}^{p}}\) on the unit ball. In passing, we recover (and somehow simplify the proof of) parts of the recent article by Demazeux, dealing with the same question for H1 of the unit disc. We also estimate the essential norm of a composition operator acting on \({A_{\alpha}^{p}}\) in terms of the angular derivatives of \({\phi}\), under a mild condition on \({\phi}\).