A nicely behaved singular integral on a purely unrectifiable set
Author:
Petri Huovinen
Journal:
Proc. Amer. Math. Soc. 129 (2001), 33453351
MSC (2000):
Primary 28A75, 42B20; Secondary 30E20
Published electronically:
April 2, 2001
MathSciNet review:
1845012
Fulltext PDF Free Access
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Abstract: We construct an example of a purely 1unrectifiable ADregular set in the plane such that the limit
exists and is finite for almost every for some class of antisymmetric CalderónZygmund kernels. Moreover, the singular integral operators associated with these kernels are bounded in , where has a positive measure.
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 X. Tolsa, Principal values for the Cauchy integral and rectifiability, Proc. Amer. Math. Soc. 128 2000, pp. 21112119. CMP 2000:14
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Additional Information
Petri Huovinen
Affiliation:
Department of Mathematics, University of Jyväskylä, P.O. Box 35, FIN40351 Jyväskylä, Finland
Email:
pjh@math.jyu.fi
DOI:
http://dx.doi.org/10.1090/S000299390105955X
PII:
S 00029939(01)05955X
Keywords:
Singular integrals,
rectifiability
Received by editor(s):
August 31, 1999
Received by editor(s) in revised form:
March 22, 2000
Published electronically:
April 2, 2001
Additional Notes:
The author was supported by EU TMR Grant #ERBFMBICT972410
Communicated by:
David Preiss
Article copyright:
© Copyright 2001
American Mathematical Society
