JournalsrmiVol. 37, No. 5pp. 1861–1884

A quantitative stability theorem for convolution on the Heisenberg group

  • Kevin O'Neill

    University of California Davis, USA
A quantitative stability theorem for convolution on the Heisenberg group cover
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Abstract

Although the convolution operators on Euclidean space and the Heisenberg group satisfy the same LpL^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.

Cite this article

Kevin O'Neill, A quantitative stability theorem for convolution on the Heisenberg group. Rev. Mat. Iberoam. 37 (2021), no. 5, pp. 1861–1884

DOI 10.4171/RMI/1250