Interpolation of 𝑙^{𝑞} sequences by 𝐻^{𝑝} functions

Taylor, B. A.; Williams, D. L.

doi:10.1090/S0002-9939-1972-0294652-X

Interpolation of $l^{q}$ sequences by $H^{p}$ functions
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by B. A. Taylor and D. L. Williams PDF

Proc. Amer. Math. Soc. 34 (1972), 181-186 Request permission

Abstract:

It is pointed out that the method used by L. Carleson to study interpolation by bounded analytic functions applies to the study of the analogous problem for ${H^p}$ functions. In particular, there exist sequences of points in the unit disc which are not uniformly separated, but which are such that every ${l^q}$ sequence can be interpolated along this sequence by an ${H^p}$ function $(1 \leqq p \leqq q \leqq + \infty )$.

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