JournalsrmiVol. 13, No. 2pp. 361–376

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

  • Yurii I. Lyubarskii

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

    University of Trondheim, Norway
Complete interpolating sequences for Paley-Wiener spaces and Muckenhoupt's ($A_p$) condition cover
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Abstract

We describe the complete interpolating sequences for the Paley-Wiener spaces Lπp(1<p<)L^p_\pi (1 < p < \infty) in terms of Muckenhoupt's (ApA_p) condition. For p=2p=2, this description coincides with those given by Pavlov [9], Nikol'skii [8], and Minkin [7] of the unconditional bases of complex exponentials in L2(π,π)L^2 (– \pi , \pi). While the techniques of these authors are linked to the Hilbert space geometry of Lπ2L^2_\pi, our method of proof is based on turning the problem into one about boundedness of the Hilbert transform in certain weighted LpL^p spaces of functions and sequences.

Cite this article

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

DOI 10.4171/RMI/224