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Article overview
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Bergman-type Singular Integral Operators and Applications | | Alexander Volberg
; Brett D. Wick
; | | Date: |
7 Oct 2009 | | Abstract: | The purposes of this paper are two fold. 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 $B^sigma_2(mathbb{B}_n)$. In particular, we demonstrate that for
any $sigmageq 0$, 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. | | Source: | arXiv, 0910.1142 | | Services: | Forum | Review | PDF | Favorites | |
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