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Southeastern Analysis Meeting
March 5-9, 2008
Vanderbilt University
Nashville, Tennessee, USA

Organizers
Brett Wick, Daoxing Xia, Dechao Zheng

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Boundedness and Compactness of Hankel Operators on the Sphere
by
Jingbo Xia
SUNY at Buffalo

Let S be the unit sphere in Cn and let ds be the spherical measure on S. Recall that the Hankel operator Hf is defined by the formula Hf = (1 - P)Mf|H2(S), where H2(S) is the Hardy space on S and P: L2(S, ds) → H2(S) is the orthogonal projection. We show that a large amount of information about the function f - Pf can be recovered from the properties of the Hankel operator Hf. For example, if Hf is compact, then the function f - Pf is necessarily in VMO.

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Date received: January 14, 2008

Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cavq-10.