Extensions of the classical Cesaro operator on Hardy spaces
Keyword(s):
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 $X$.
2016 ◽
Vol 86
(1)
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pp. 97-112
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1999 ◽
Vol 42
(2)
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pp. 139-148
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2002 ◽
Vol 65
(2)
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pp. 177-182
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2008 ◽
Vol 340
(2)
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pp. 1180-1203
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2017 ◽
Vol 69
(2)
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pp. 263-281
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2005 ◽
Vol 129
(4)
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pp. 4022-4039
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2018 ◽
Vol 43
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pp. 521-530
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2019 ◽
Vol 44
(2)
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pp. 601-613
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