Extensions of the classical Cesaro operator on Hardy spaces

Authors

  • Guillermo P. Curbera
  • Werner J. Ricker

DOI:

https://doi.org/10.7146/math.scand.a-15172

Abstract

For each 1p<, the classical Cesàro operator C from the Hardy space Hp to itself has the property that there exist analytic functions fHp 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.

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Published

2011-06-01

How to Cite

Curbera, G. P., & Ricker, W. J. (2011). Extensions of the classical Cesaro operator on Hardy spaces. MATHEMATICA SCANDINAVICA, 108(2), 279–290. https://doi.org/10.7146/math.scand.a-15172

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Articles