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Given 0 < p,q < ∞ and any sequence z = zₙ in the unit disc , we define an operator from functions on to sequences by . Necessary and sufficient conditions on zₙ are given such that maps the Hardy space boundedly into the sequence space . A corresponding result for Bergman spaces is also stated.
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 -