Bounded evaluation operators from $H^p$ into $\ell^q$
Volume 179 / 2007
Studia Mathematica 179 (2007), 1-6
MSC: Primary 30H05, 46E15.
DOI: 10.4064/sm179-1-1
Abstract
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.
