WEIGHTED COMPOSITION OPERATORS (1+ϵ)φ_(r ) ON BERGMAN TYPE SPACES 〖 A〗_(z+ϵ)^(1+ϵ) WITH DOUBLE WEIGHTED (z+ϵ)

Abstract

This study investigates the boundedness , compactness, essential norm and the Schatten class of weighted composition operators (1+ϵ)C_(φ_r ) on Bergman types spaces A_(z+ϵ)^(1+ϵ) with double weight (z+ϵ). Let X=(1+ϵ)∈H(D):(1+ϵ)C_(φ_r ) :A_(z+ϵ)^(1+ϵ)→A_(z+ϵ)^(1+ϵ) is bounded. For some regular weights (z+ϵ), the researcher obtains that X=H^∞ if and only if φ_r is a finite Blaschke product.