Representation formulae for the higher-order Steklov and $L^{2^m}$-Friedrichs inequalities

In this paper, we obtain remainder term representation formulae for the higher-order Steklov inequality for vector fields which imply short and direct proofs of the sharp (classical) Steklov inequalities. The obtained results directly imply sharp Steklov type inequalities for some vector fields satisfying Hörmander’s condition, for example. We also give representation formulae for the $L^{2^m}$-Friedrichs inequalities for vector fields.

Keywords

Steklov inequality, Friedrichs inequality, remainder term, vector fields

2010 Mathematics Subject Classification

22E30, 39B62, 39B99

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Received 29 May 2020

Accepted 5 September 2023

Published 7 August 2024