Journal of Lie Theory

no. 4
Lp-Boundedness of Flag Kernels on Homogeneous Groups via Symbolic Calculus
Journal of Lie Theory, Volume 23 (2013) no. 4, pp. 953-977
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.
DOI: 10.5802/jolt.759
Classification: 42B20, 42B25
Keywords: Homogeneous groups, singular integrals, multipliers, flag kernels, Fourier transform, maximal functions, L-p-spaces, Littlewood-Paley theory 
@article{JOLT_2013_23_4_a3,
     author = {P. Glowacki},
     title = {L\protect\textsuperscript{p}-Boundedness of {Flag} {Kernels} on {Homogeneous} {Groups} via {Symbolic} {Calculus}},
     journal = {Journal of Lie Theory},
     pages = {953--977},
     year = {2013},
     volume = {23},
     number = {4},
     doi = {10.5802/jolt.759},
     zbl = {1292.43009},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.759/}
}
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P. Glowacki. Lp-Boundedness of Flag Kernels on Homogeneous Groups via Symbolic Calculus. Journal of Lie Theory, Volume 23 (2013) no. 4, pp. 953-977. doi: 10.5802/jolt.759

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