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arXiv · 1703.00181

Littlewood-Paley theory for triangle buildings

Tim Steger·Bartosz Trojan
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Abstract

For the natural two parameter filtration $(\mathcal{F}_\lambda : \lambda \in P)$ on the boundary of a triangle building we define a maximal function and a square function and show their boundedness on $L^p(\Omega_0)$ for $p \in (1, \infty)$. At the end we consider $L^p(\Omega_0)$ boundedness of martingale transforms. If the building is of $\text{GL}(3, \mathbb{Q}_p)$ then $\Omega_0$ can be identified with $p$-adic Heisenberg group.

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Tim Steger, Bartosz Trojan. 2017-03-01. Littlewood-Paley theory for triangle buildings. https://doi.org/10.1007/s12220-017-9856-6

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