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Abstract
We show that for any 1<p<∞, the space Hankp(R+)⊆B(Lp(R+)) of all Hankel operators on Lp(R+) is equal to the w∗closure of the linear span of the operators θu:Lp(R+)→Lp(R+) defined by θuf=f(u−⋅), for u>0. We deduce that Hankp(R+) is the dual space ofAp(R+), a halfline analogue of the FigaTalamencaHerz algebra Ap(R). Then we show that a function m:R∗+→C is the symbol of a pcompletely bounded multiplier Hankp(R+)→Hankp(R+) if and only if there exist α∈L∞(R+;Lp(Ω)) and β∈L∞(R+;Lp′(Ω)) such that m(s+t)=⟨α(s),β(t)⟩ for a.e. (s,t)∈R∗2+. We also give analogues of these results in the (easier) discrete case.
Original language  English 

Journal  Pacific Journal of Mathematics 
DOIs  
Publication status  Accepted/In press  12 Apr 2024 
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Dive into the research topics of 'Hankel operators on L^p(ℝ_+) and their pcompletely bounded multipliers'. Together they form a unique fingerprint.Projects
 1 Finished

Completely Bounded Fourier Multipiers on Hardy Spaces
Zadeh, S. (Principal Investigator)
26/01/22 → 3/02/22
Project: Research