Geodesic
Bounded evaluation operators from $H^p$ into $\ell^q$
Martin Smith 1
1 Department of Mathematics University of York York Y010 5DD United Kingdom and Greenhead College Greenhead Road Huddersfield West Yorkshire HD1 4ES, United Kingdom
Studia Mathematica, Tome 179 (2007) no. 1, pp. 1-6 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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Given $0 p,q \infty$ and any sequence ${\bf z} = \{z_n\}$ in the unit disc ${\bf D}$, we define an operator from functions on ${\bf D}$ to sequences by $T_{{\bf z},p}(f) = \{(1-|z_n|^2)^{1/p}f(z_n)\}$. Necessary and sufficient conditions on $\{z_n\} $ are given such that $T_{{\bf z},p}$ maps the Hardy space $H^p$ boundedly into the sequence space $\ell^q$. A corresponding result for Bergman spaces is also stated.
DOI : 10.4064/sm179-1-1
Keywords: given infty sequence unit disc define operator functions sequences n necessary sufficient conditions given maps hardy space boundedly sequence space ell corresponding result bergman spaces stated

Martin Smith  1

1 Department of Mathematics University of York York Y010 5DD United Kingdom and Greenhead College Greenhead Road Huddersfield West Yorkshire HD1 4ES, United Kingdom 
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Martin Smith. Bounded evaluation operators from $H^p$ into $\ell^q$. Studia Mathematica, Tome 179 (2007) no. 1, pp. 1-6. doi: 10.4064/sm179-1-1

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