A nicely behaved singular integral on a purely unrectifiable set

Author:
Petri Huovinen

Journal:
Proc. Amer. Math. Soc. **129** (2001), 3345-3351

MSC (2000):
Primary 28A75, 42B20; Secondary 30E20

Published electronically:
April 2, 2001

MathSciNet review:
1845012

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

We construct an example of a purely 1-unrectifiable AD-regular set in the plane such that the limit

exists and is finite for almost every for some class of antisymmetric Calderón-Zygmund kernels. Moreover, the singular integral operators associated with these kernels are bounded in , where has a positive measure.

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Additional Information

**Petri Huovinen**

Affiliation:
Department of Mathematics, University of Jyväskylä, P.O. Box 35, FIN-40351 Jyväskylä, Finland

Email:
pjh@math.jyu.fi

DOI:
https://doi.org/10.1090/S0002-9939-01-05955-X

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