Complete interpolating sequences for Paley-Wiener spaces and Muckenhoupt's ($A_p$) condition
Complete interpolating sequences for Paley-Wiener spaces and Muckenhoupt's ($A_p$) condition
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DOI：
10.4171/rmi/224
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发表时间：
1995-11
影响因子：
1.2
通讯作者：
Yurii Lyubarskii;K. Seip
中科院分区：
文献类型：
--
作者：
Yurii Lyubarskii;K. Seip
本文利用Muckenhoupt（Ap）条件描述了Paley-Wiener空间Lpp（1 < p < 8）的完备插值序列.当p = 2时，这种描述与Pavlov [9]，Nikol'skii [8]和Minkin [7]对L2（-p，p）中复指数的无条件基的描述一致。虽然这些作者的技术是链接到希尔伯特空间几何的Lp 2，我们的方法的证明是基于把问题变成一个关于有界性的希尔伯特变换在某些加权Lp空间的功能和序列。
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.