Essential normality for certain weighted composition operators on the Hardy space $H^{2}$

Abstract

We characterize the essentially normal weighted composition operators $Cpsivarphi$ on the Hardy space $H^{2}$ , whenever $varphi$is a linear-fractional transformation and ψ ∈ A$(Bbb{D})$ . Also we investigate the essential normality problem for some other weighted composition operators on $H^{2}$ .