Optimal domain of Volterra operators in Korenblum spaces

The aim of this article is to study the largest domain space [T,X], whenever it exists, of a given continuous linear operator T:X→X, where X⊆H(D) is a Banach space of analytic functions on the open unit disc D⊆C. That is, [T,X]⊆H(D) is the largest Banach space of analytic functions containing X to which T has a continuous, linear, X-valued extension T:[T,X]→X. The class of operators considered consists of generalized Volterra operators T acting in the Korenblum growth Banach spaces X:=A^{−γ}, for γ>0. Previous studies dealt with the classical Cesàro operator T:=C acting in the Hardy spaces Hp, 1≤p<∞, [18], [19], in A^{−γ}, [3], and more recently, generalized Volterra operators T acting in X:=Hp.