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

Andreas Hartmann (1)

1 IMB - Institut de Mathématiques de Bordeaux

Given a sequence of points in the unit disk, a well known result due to Carleson states that if it is possible to interpolate the value one in any 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). 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.

Mots clés: Hardy spaces; Interpolating sequences; Weak interpolation

Domaines: Variables complexes [math.CV]

Andreas Hartmann. Extremely weak interpolation in $H^{\infty}$. 2010. ⟨hal-00526930v1⟩