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Article Dans Une Revue Proceedings of the American Mathematical Society Année : 2012

Extremely weak interpolation in $H^{\infty}$

Andreas Hartmann

Résumé

Given a sequence of points in the unit disk, a well known result due to Carleson states that if given any point of the sequence it is possible to interpolate the value one in that point and zero in all the other points of the sequence, with uniform control of the norm in the Hardy space of bounded analytic functions on the disk, then the sequence is an interpolating sequence (i.e.\ every bounded sequence of values can be interpolated by functions in the Hardy space). It turns out that such a result holds in other spaces. In this short note we would like to show that for a given sequence it is sufficient to find just {\bf one} function interpolating suitably zeros and ones to deduce interpolation in the Hardy space.
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Dates et versions

hal-00526930 , version 1 (17-10-2010)
hal-00526930 , version 2 (18-10-2010)

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Citer

Andreas Hartmann. Extremely weak interpolation in $H^{\infty}$. Proceedings of the American Mathematical Society, 2012, 140, pp.2411-2416. ⟨hal-00526930v2⟩

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