Authors
Citation
T. Tao, The weak-type (1,1) of LlogL homogeneous convolution operator, INDI MATH J, 48(4), 1999, pp. 1547-1584
Citations number
10
Categorie Soggetti
Mathematics
Journal title
INDIANA UNIVERSITY MATHEMATICS JOURNAL
ISSN journal
00222518
→ ACNP
Volume
48
Issue
4
Year of publication
1999
Pages
1547 - 1584
Database
ISI
SICI code
0022-2518(199924)48:4<1547:TW(OLH>2.0.ZU;2-R
Abstract
We show that a homogeneous convolution kernel on an arbitrary homogeneous g
roup which is LlogL on the unit annulus is bounded on L-p for 1 < p < infin
ity and is of weak-type (1, 1), generalizing the result of Seeger [9]. The
proof is in a similar spirit to that of Christ and Rubio de Francia [3].