This paper presents an approach, based on interpolation theory of operators, to the study of interpolating sequences for interpolation Banach spaces between Hardy spaces. It is shown that the famous Carleson result for H∞ can be lifted to a large class of abstract Hardy spaces. A description is provided of the range of the Carleson operator defined on interpolation spaces between the classical Hardy spaces in terms of uniformly separated sequences. A key role in this description is played by some general interpolation results proved in the paper. As by-products, novel results are obtained which extend the Shapiro–Shields result on the characterisation of interpolation sequences for the classical Hardy spaces Hp. Applications to Hardy–Lorentz, Hardy–Marcinkiewicz and Hardy–Orlicz spaces are presented.

本文提出了一种基于算子插值理论的方法来研究Hardy空间之间插值Banach空间的插值序列。结果表明， H ∞的著名 Carleson 结果可以提升到一大类抽象哈代空间。根据一致分离的序列，描述了在经典 Hardy 空间之间的插值空间上定义的 Carleson 算子的范围。文中证明的一些通用插值结果在这种描述中起着关键作用。作为副产品，获得了新的结​​果，扩展了 Shapiro-Shields 对经典哈代空间H p的插值序列的表征的结果. 介绍了在 Hardy–Lorentz、Hardy–Marcinkiewicz 和 Hardy–Orlicz 空间中的应用。