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arXiv · 1907.11986

A Quantitative Stability Theorem for Convolution on the Heisenberg Group

Kevin O'Neill
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Abstract

Although convolution on Euclidean space and the Heisenberg group satisfy the same $L^p$ bounds with the same optimal constants, the former has maximizers while the latter does not. However, as work of Christ has shown, it is still possible to characterize near-maximizers. Specifically, any near-maximizing triple of the trilinear form for convolution on the Heisenberg group must be close to a particular type of triple of ordered Gaussians after adjusting by symmetry. In this paper, we use the expansion method to prove a quantitative version of this characterization.

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Kevin O'Neill. 2019-07-27. A Quantitative Stability Theorem for Convolution on the Heisenberg Group. https://arxiv.org/abs/1907.11986

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