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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

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


Authors: B. A. Taylor and D. L. Williams
Journal: Proc. Amer. Math. Soc. 34 (1972), 181-186
MSC: Primary 30A78
DOI: https://doi.org/10.1090/S0002-9939-1972-0294652-X
MathSciNet review: 0294652
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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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Keywords: Interpolation, <IMG WIDTH="33" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="${H^p}$"> spaces, analytic functions, subharmonic functions
Article copyright: © Copyright 1972 American Mathematical Society