Lacunary elliptic maximal operator on the Heisenberg group

Joonil Kim; Jeongtae Oh

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arXiv · 2501.11928

Lacunary elliptic maximal operator on the Heisenberg group

Joonil Kim·Jeongtae Oh

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Abstract

In this paper, we prove $ L^p $ boundedness results for lacunary elliptic maximal operators on the Heisenberg group. Furthermore, we extend these $ L^p $ estimates from skew-symmetric matrices, which naturally arise in Heisenberg group operations, to arbitrary matrices $ A $, investigating how the curvature induced by $ A $ governs the $ L^p $ boundedness of lacunary circular and elliptic maximal operators. Specifically, we provide necessary and sufficient conditions on $ A $ that determine whether these operators are bounded or unbounded on $ L^p $.

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BibTeX RIS

Joonil Kim, Jeongtae Oh. 2025-01-21. Lacunary elliptic maximal operator on the Heisenberg group. https://arxiv.org/abs/2501.11928

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