Revista Matemática Iberoamericana


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Volume 13, Issue 2, 1997, pp. 361–376
DOI: 10.4171/RMI/224

Published online: 1997-08-31

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

Yurii I. Lyubarskii[1] and Kristian Seip[2]

(1) The Norwegian University of Science and Technology, Trondheim, Norway
(2) University of Trondheim, Norway

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.

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Lyubarskii Yurii, Seip Kristian: Complete interpolating sequences for Paley-Wiener spaces and Muckenhoupt's ($A_p$) condition. Rev. Mat. Iberoamericana 13 (1997), 361-376. doi: 10.4171/RMI/224