COMPLETE INTERPOLATING SEQUENCES

FOR PALEY-WIENER SPACES AND

MUCKENHOUPT’S (A_{p}) CONDITION

Yurii I. Lyubarskii Kristian Seip

Abstract. We describe the complete interpolating sequences for the Paley-Wiener spaces L_{π}^{p} (1 < p < ∞) in terms of Muckenhoupt’s (A_{p}) condition. For p = 2, this description coincides with those given by Pavlov (1979), Nikol’skii (1980), and Minkin (1992) of the unconditional bases of complex exponentials in L^{2}(−π, π). While the techniques of these authors are linked to the Hilbert space geometry of L_{π}^{2}, 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.

Typeset by AMS-TEX