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arXiv · 2305.04700

Lacunary maximal functions on homogeneous groups

Aswin Govindan Sheri·Jonathan Hickman·James Wright
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Abstract

We observe that classical arguments of Ricci--Stein can be used to prove $L^p$ bounds for maximal functions associated to lacunary dilates of a fixed measure in the setting of homogenous groups. This recovers some recent results on averages over Kor\'anyi spheres and horizontal spherical averages of a type introduced by Nevo--Thangavelu. Moreover, the main theorem applies much more broadly and we explore its consequences through a variety of explicit examples.

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Aswin Govindan Sheri, Jonathan Hickman, James Wright. 2023-05-08. Lacunary maximal functions on homogeneous groups. https://arxiv.org/abs/2305.04700

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