Complete interpolating sequences for Paley-Wiener spaces and Muckenhoupt's $(A_p)$ condition

Abstract

We describe the complete interpolating sequences for the Paley-Wiener spaces $L^p_π$ ($1<p<\infty$) in terms of Muckenhoupt&#39;s $(A_p)$ condition. For $p=2$, this description coincides with those given by Pavlov (1979), Nikol&#39;skii (1980), and Minkin (1992) of the unconditional bases of complex exponentials in $L^2(-π,π)$. While the techniques of these authors are linked to the Hilbert space geometry of $L^2_π$, our method of proof is based on turning the problem into one about boundedness of the Hilbert transform in certain weighted $L^p$ spaces of functions and sequences.