2025/02/02 by Albanese, Angela A., Bonet, José, Ricker, Werner J.
#47A10 #47A16 #47A35 #47A35 47A16 #47B38 #FOS: Mathematics #Functional Analysis (math.FA) #Primary 46E15 #Secondary 46E10
paper · doi:10.48550/arxiv.2502.00755
The aim of this article is to study the largest domain space [T,X], whenever it exists, of a given continuous linear operator T\colon X→ X, where X⊆ H(\mathbbD) is a Banach space of analytic functions on the open unit disc \mathbbD⊆ ℂ. That is, [T,X]⊆ H(\mathbbD) is the largest Banach space of analytic functions containing X to which T has a continuous, linear, X-valued extension T\colon [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<∞, \citeCR, \citeCR1, in A-γ, \citeABR-R, and more recently, generalized Volterra operators T acting in X:=Hp, \citeBDNS.