Journal Home Page

Cumulative Index

List of all Volumes

Complete Contents
of this Volume

Previous Article

Next Article

Journal of Lie Theory 23 (2013), No. 4, 953--977
Copyright Heldermann Verlag 2013

Lp-Boundedness of Flag Kernels on Homogeneous Groups via Symbolic Calculus

Pawel Glowacki
Institute of Mathematics, University of Wroclaw, pl. Grunwaldzki 2/4, 51-386 Wroclaw, Poland

We prove that the flag kernel singular integral operators of Nagel-Ricci-Stein on a homogeneous group are bounded on Lp, 1<p<∞. The gradation associated with the kernels is the natural gradation of the underlying Lie algebra. Our main tools are the Littlewood-Paley theory and a symbolic calculus combined in the spirit of Duoandikoetxea and Rubio de Francia.

Keywords: Homogeneous groups, singular integrals, multipliers, flag kernels, Fourier transform, maximal functions, L-p-spaces, Littlewood-Paley theory.

MSC: 42B20, 42B25

[ Fulltext-pdf  (377  KB)] for subscribers only.