WEIGHTED COMPOSITION OPERATORS (1+ϵ)φ_(r ) ON BERGMAN TYPE SPACES 〖 A〗_(z+ϵ)^(1+ϵ) WITH DOUBLE WEIGHTED (z+ϵ)
Prepared by the researche : Dr. BUSHARA EISA HAMAD ABDALLA – Assistant of professor Mathematics, Department of Mathematics – White Nile University, Kosti, Sudan
Democratic Arabic Center
Journal of Afro-Asian Studies : Twenty-Third Issue – November 2024
A Periodical International Journal published by the “Democratic Arab Center” Germany – Berlin
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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.
