Mathematical Research Letters

Volume 11, Issue 5, September 2004 pp. 599-614.

lacunary directional maximal function on the Heisenberg group

Authors: Joonil Kim
Author institution: Chung-Ang University

Summary: 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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