Mathematical Research Letters

Volume 11 (2004)

Number 5

lacunary directional maximal function on the Heisenberg group

Pages: 599 – 614

DOI: http://dx.doi.org/10.4310/MRL.2004.v11.n5.a5

Author

Joonil Kim (Chung-Ang University)

Abstract

We prove the $L^p$ boundedness of the maximal function along a family of lines $\{t(2^{k_1},2^{k_2},2^{k_3})\}$ on the Heisenberg group $\mathbb{H}^1$. The proof is based on the group Fourier transform and the angular Littlewood-Paley decompositions in the Heisenberg group in [7].

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