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

• Autorzy: Martin Smith
• Języki publikacji: EN

Abstrakty

EN

Given 0 < p,q < ∞ and any sequence z = {zₙ} in the unit disc 𝔻, we define an operator from functions on 𝔻 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.

Kategorie tematyczne

• 46E15: Banach spaces of continuous, differentiable or analytic functions
• 30H05: Bounded analytic functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2007
• Tom: 179
• Numer: 1
• Strony: 1-6

Daty

wydano

2007

Twórcy

autor

Martin Smith

• Department of Mathematics, University of York, York Y010 5DD, United Kingdom
• Greenhead College, Greenhead Road, Huddersfield, West Yorkshire, HD1 4ES, United Kingdom

Identyfikatory

DOI

10.4064/sm179-1-1