Journal of Operator Theory

Volume 35, Issue 2, Spring 1996 pp. 271-316.

Une approche de l’interpolation libre généralisée par la théorie des opérateurs et caractérisation des traces $H^p |_\Lambda $

Authors: Andreas Hartmann
Author institution:Université Bordeaux I, UFR Mathématiques/Informatique, 351, Cours de la Libération, 33405 Talence Cédex, FRANCE

Summary: We prove the necessity and sufficiency of the generalized Carleson condition (CG) for free interpolation in the Hardy spaces H^p, $1 < p \le \infty$, by identifying scalar operator interpolation, unconditional bases and condition (CG). For this type of interpolation, N.K. Nikolskii and S.V. Khrushchëv have announced without proof a characterization of the data space of interpolable function sequences. We give the proof for this conjecture and apply the result to the characterization of the trace space $H^p \left| {_\Lambda } \right.$, where $\Lambda$ is a finite union of interpolating sequences, generalizing a result of V.I. Vasyunin. We finish with the explicit construction of a linear continuous operator of interpolation.

Keywords: Free interpolation, Hardy spaces, interpolating sequences, lifting of the commutant, Nehari’s theorem, unconditional bases.

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