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

### Yurii I. Lyubarskii

The Norwegian University of Science and Technology, Trondheim, Norway### Kristian Seip

University of Trondheim, Norway

## Abstract

We describe the complete interpolating sequences for the Paley-Wiener spaces $L^p_\pi (1 < p < \infty)$ in terms of Muckenhoupt's ($A_p$) condition. For $p=2$, this description coincides with those given by Pavlov [9], Nikol'skii [8], and Minkin [7] of the unconditional bases of complex exponentials in $L^2 (– \pi , \pi)$. While the techniques of these authors are linked to the Hilbert space geometry of $L^2_\pi$, 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.

## Cite this article

Yurii I. Lyubarskii, Kristian Seip, Complete interpolating sequences for Paley-Wiener spaces and Muckenhoupt's ($A_p$) condition. Rev. Mat. Iberoam. 13 (1997), no. 2, pp. 361–376

DOI 10.4171/RMI/224