Extensions of the classical Cesaro operator on Hardy spaces

  • Guillermo P. Curbera
  • Werner J. Ricker

Abstract

For each $1\le p<\infty$, the classical Cesàro operator $\mathcal C$ from the Hardy space $H^p$ to itself has the property that there exist analytic functions $f\notin H^p$ with ${\mathcal C}(f)\in H^p$. This article deals with the identification and properties of the (Banach) space $[{\mathcal C}, H^p]$ consisting of all analytic functions that $\mathcal C$ maps into $H^p$. It is shown that $[{\mathcal C}, H^p]$ contains classical Banach spaces of analytic functions $X$, genuinely bigger that $H^p$, such that $\mathcal C$ has a continuous $H^p$-valued extension to $X$. An important feature is that $[{\mathcal C}, H^p]$ is the largest amongst all such spaces $X$.
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
Section
Articles