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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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Cartan type estimates for Riesz transforms
by
Vladimir Eiderman
Michigan State University
Coauthors: Fedor Nazarov and Alexander Volberg
For given complex numbers n1, ..., nN, and points y1, ..., yN, in Rd, d ≥ 2, we define the set
|
Zs(P, n)={x ∈ Rd:| |
N
å
j=1
|
|
x-yj
|x-yj|s+1
|
nj| > P}, s > 0, P > 0. |
|
Our goal is to give sharp upper bounds for the size of Zs(P, n). This size will be measured by the
Hausdorff content Mh with various gauge functions h.
Among other things, we shall characterize all h for which the estimates do not blow up as N→∞. In this case a routine limiting arguments
allow us to extend our bounds to s-Riesz transforms of all finite Borel measures.
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Date received: February 11, 2008
Copyright © 2008 by the author(s).
The author(s) of this document and the organizers of the conference
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Atlas Conferences Inc.
Document # cavq-43.