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

By Nicola Arcozzi, Richard Rochberg, Eric T. Sawyer. 2007

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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

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e8ac8bf1464a44001ccdeea65869dc47cb6d059f

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In Applied Mathematics

In Mathematical Physics

Citations in the corpus

On the Isomorphism Problem for Multiplier Algebras of Nevanlinna-Pick Spaces (2015, background): “_e existence of algebraic isomorphisms is also quite well understood for multiplier algebras associated with certain one-dimensional varieties under the assumption of suõcient regularity on the boundary [4, 5,27].”
Operator Theory and Function Theory in Drury–Arveson Space and Its Quotients (2013, methodology): “A characterization of the Carleson measures of B p (Bd) for ranges of p and σ that include p = 2, σ = 1/2 was obtained in [13],[114] and [121].”
Bergman-type singular integral operators and the characterization of Carleson measures for Besov-Sobolev spaces on the complex ball (2009, methodology): “It is not at all clear how (or if it is even possible) to adapt the methods of [1, 15, 16] to address the more general case of 1 2 < σ < d 2 .”