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
glowacki@math.uni.wroc.pl
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
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