Complete interpolating sequiences for Paley-Wiener spaces and Muckenhoupt's (Ap) condition

• Autores: Yurii I. Lyubarskii, Kristian Seip
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 13, Nº 2, 1997, págs. 361-376
• Idioma: inglés
• Títulos paralelos:
  • Series de interpolación completas para espacios de Paley-Wiener y condición (Ap) de Muckenhoupt.
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• Resumen

  • We describe the complete interpolating sequences for the Paley-Wiener spaces Lpp (1 < p < 8) in terms of Muckenhoupt's (Ap) 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 L2(-p,p). While the techniques of these authors are linked to the Hilbert space geometry of Lp2, our method of proof is based in turning the problem into one about boundedness of the Hilbert transform in certain weighted Lp spaces of functions and sequences.