Extensions of the classical Cesaro operator on Hardy spaces

• Autores: Guillermo Curbera Costello, Werner J. Ricker
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 108, Nº 2, 2011, págs. 279-290
• Idioma: inglés
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• Resumen

  • 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.