Revista Matemática Iberoamericana
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Published online: 1997-08-31
Complete interpolating sequences for Paley-Wiener spaces and Muckenhoupt's ($A_p$) conditionYurii I. Lyubarskii and Kristian Seip (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 , Nikol'skii , and Minkin  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