Resumen de Extensions of the classical Cesaro operator on Hardy spaces

Guillermo Curbera Costello, Werner J. Ricker

• For each 1≤p<∞, the classical Cesàro operator C from the Hardy space Hp to itself has the property that there exist analytic functions f∉Hp with C(f)∈Hp. This article deals with the identification and properties of the (Banach) space [C,Hp] consisting of all analytic functions that C maps into Hp. It is shown that [C,Hp] contains classical Banach spaces of analytic functions X, genuinely bigger that Hp, such that C has a continuous Hp-valued extension to X. An important feature is that [C,Hp] is the largest amongst all such spaces X.