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Research Article | Open Access

The constant in the Sobolev inequality and the boundedness of subelliptic operators on compact Lie groups

Andrea V. Hurtado-Quiceno1, Duván Cardona Sánchez2( )
Department of Mathematics, RPTU Kaiserslautern-Landau, Gottlieb-Daimler-Straße 48, 67663 Kaiserslautern, Germany
Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Krijgslaan 281, Building S8, B-9000 Ghent, Belgium
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Abstract

Given a compact connected Lie group G, we estimated the constant for the Sobolev inequality for an arbitrary Hörmander sub-Laplacian on G. The constant was estimated in terms of quantities depending on the intrinsic geometry of the group and on the Lebesgue parameters. We also provided applications of this result to the estimation of the operator norm for L p - L q -bounded subelliptic pseudo-differential operators in subelliptic Hörmander classes.

Keywords

compact Lie groupsSobolev inequalitysubelliptic pseudo-differential operators
CLC number: 26D10, 43A80, 46E35

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Communications in Analysis and Mechanics
Volume 17 Issue 4,
December 2025
Pages 878-897
DOI: 10.3934/cam.2025035

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Hurtado-Quiceno AV, Sánchez DC. The constant in the Sobolev inequality and the boundedness of subelliptic operators on compact Lie groups. Communications in Analysis and Mechanics, 2025, 17(4): 878-897. https://doi.org/10.3934/cam.2025035

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Received: 21 January 2025
Revised: 11 September 2025
Accepted: 16 September 2025
Published: 15 December 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)