Interpolating sequences for weighted spaces of analytic functions on the unit ball of a Hilbert space
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We show that an interpolating sequence for the weighted Banach space of analytic functions on the unit ball of a Hilbert space is hyperbolically separated. In the case of the so-called standard weights, a sufficient condition for a sequence to be linear interpolating is given in terms of Carleson type measures. Other conditions to be linearly interpolating are provided as well. Our results apply to the space of Bloch functions of such unit ball.
KeywordsInterpolating sequence Hyperbolically separated Bloch function in the ball Infinite dimensional holomorphy Weighted space of analytic functions
Mathematics Subject ClassificationPrimary 30D45 46E50 Secondary 46G20
This paper was completed during the 2016 fall semester while Mikael Lindström was visiting Universidad de Valencia whose hospitality is gratefully acknowledged with special thanks to Pablo Galindo. We warmly thank the referees for their very careful reading and the suggestions provided.
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