A nicely behaved singular integral on a purely unrectifiable set

Authors
Huovinen, P
Citation
P. Huovinen, A nicely behaved singular integral on a purely unrectifiable set, P AM MATH S, 129(11), 2001, pp. 3345-3351
Citations number
10
Categorie Soggetti
Mathematics
Journal title
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
ISSN journal
00029939 → ACNP
Volume
129
Issue
11
Year of publication
2001
Pages
3345 - 3351
Database
ISI
SICI code
0002-9939(2001)129:11<3345:ANBSIO>2.0.ZU;2-A
Abstract
We construct an example of a purely 1-unrectifiable AD-regular set E in the plane such that the limit [GRAPHIC] exists and is finite for H-1 almost every x is an element of E for some cla ss of antisymmetric Calderon-Zygmund kernels. Moreover, the singular integr al operators associated with these kernels are bounded in L-2(F), where F s ubset of E has a positive H-1 measure.