Carleson measures for the Drury-Arveson Hardy space and other Besov-Sobolev spaces on complex balls

• Autores: Nicola Arcozzi, Richard Rochberg, Eric Sawyer
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 218, Nº 4, 2008, págs. 1107-1180
• Idioma: inglés
• DOI: 10.1016/j.aim.2008.03.001
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• Resumen

  • For 0s<1/2 we characterize Carleson measures µ for the analytic Besov�Sobolev spaces on the unit ball in by the discrete tree condition on the associated Bergman tree . Combined with recent results about interpolating sequences this leads, for this range of s, to a characterization of universal interpolating sequences for and also for its multiplier algebra.

    However, the tree condition is not necessary for a measure to be a Carleson measure for the Drury�Arveson Hardy space . We show that µ is a Carleson measure for if and only if both the simple condition and the split tree condition hold. This gives a sharp estimate for Drury's generalization of von Neumann's operator inequality to the complex ball, and also provides a universal characterization of Carleson measures, up to dimensional constants, for Hilbert spaces with a complete continuous Nevanlinna�Pick kernel function.

    We give a detailed analysis of the split tree condition for measures supported on embedded two manifolds and we find that in some generic cases the condition simplifies. We also establish a connection between function spaces on embedded two manifolds and Hardy spaces of plane domains