Bergman-type singular integral operators and the characterization of Carleson measures for Besov-Sobolev spaces on the complex ball

By Alexander Volberg, Brett D. Wick. 2009

48 citations recorded by the source corpus.

The purposes of this paper are twofold. First, we extend the method of non-homogeneous harmonic analysis of Nazarov, Treil, and Volberg to handle "Bergman-type" singular integral operators. The canonical example of such an operator is the Beurling transform on the unit disc. Second, we use the methods developed in this paper to settle the important open question about characterizing the Carleson measures for the Besov-Sobolev space of analytic functions $B^\sigma_2$ on the complex ball of ${\Bbb{C}}^d$. In particular, we demonstrate that for any $\sigma 0$, the Carleson measures for the space are characterized by a "T1 Condition". The method of proof of these results is an extension and another application of the work originated by Nazarov, Treil, and the first author.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/c48d290c5803a95ce56aae6050f81a78001c148e

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Citations in the corpus

• GENERALIZED FRACTIONAL INTEGRALS AND THEIR COMMUTATORS OVER NON-HOMOGENEOUS METRIC MEASURE SPACES (2013, background): “ that the theory of the singular integral operators on non-homogeneous metric measure spaces arises naturally in the study of complex and harmonic analysis questions in several complex variables (see [41, 20]). More progresses on the Hardy space H1 and boundedness of operators on non-homogeneous met”