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

Martin Smith

Bounded evaluation operators from

H^{p}

into

ℓ^{q}

Martin Smith

Studia Mathematica, Tome 178 (2007), p. 1-6 / Harvested from The Polish Digital Mathematics Library

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Résumé

Given 0 < p,q < ∞ and any sequence z = zₙ in the unit disc , we define an operator from functions on to sequences by $T_{z, p} (f) = {(1 - | z ₙ | ²)}^{1 / p} f (z ₙ)$ . 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.

Publié le : 2007-01-01

Zbl 1108.30043

EUDML-ID : urn:eudml:doc:284433

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     title = {Bounded evaluation operators from $H^{p}$ into $l^{q}$
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     journal = {Studia Mathematica},
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     year = {2007},
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Martin Smith. Bounded evaluation operators from $H^{p}$ into $ℓ^{q}$
            . Studia Mathematica, Tome 178 (2007) pp. 1-6. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm179-1-1/