Bounded evaluation operators from $H^p$ into ${\ell }^q$

Martin Smith. "Bounded evaluation operators from $H^{p}$ into $ℓ^{q}$." Studia Mathematica 179.1 (2007): 1-6. <http://eudml.org/doc/284433>.

@article{MartinSmith2007,
abstract = {Given 0 < p,q < ∞ and any sequence z = zₙ in the unit disc , we define an operator from functions on to sequences by $T_\{z,p\}(f) = \{(1-|zₙ|²)^\{1/p\}f(zₙ)\}$. Necessary and sufficient conditions on zₙ are given such that $T_\{z,p\}$ maps the Hardy space $H^\{p\}$ boundedly into the sequence space $ℓ^\{q\}$. A corresponding result for Bergman spaces is also stated.},
author = {Martin Smith},
journal = {Studia Mathematica},
keywords = {Hardy space; uniformly discrete sequence; uniformly separated sequence; Bergman space},
language = {eng},
number = {1},
pages = {1-6},
title = {Bounded evaluation operators from $H^\{p\}$ into $ℓ^\{q\}$},
url = {http://eudml.org/doc/284433},
volume = {179},
year = {2007},
}

TY - JOUR
AU - Martin Smith
TI - Bounded evaluation operators from $H^{p}$ into $ℓ^{q}$
JO - Studia Mathematica
PY - 2007
VL - 179
IS - 1
SP - 1
EP - 6
AB - Given 0 < p,q < ∞ and any sequence z = zₙ in the unit disc , we define an operator from functions on to sequences by $T_{z,p}(f) = {(1-|zₙ|²)^{1/p}f(zₙ)}$. Necessary and sufficient conditions on zₙ are given such that $T_{z,p}$ maps the Hardy space $H^{p}$ boundedly into the sequence space $ℓ^{q}$. A corresponding result for Bergman spaces is also stated.
LA - eng
KW - Hardy space; uniformly discrete sequence; uniformly separated sequence; Bergman space
UR - http://eudml.org/doc/284433
ER -