Remarks on the Bernstein inequality for higher order operators and related results

Li, Dong; Sire, Yannick

doi:10.1090/tran/8708

Remarks on the Bernstein inequality for higher order operators and related results
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by Dong Li and Yannick Sire;

Trans. Amer. Math. Soc. 376 (2023), 945-967

DOI: https://doi.org/10.1090/tran/8708

Published electronically: November 4, 2022

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Abstract:

This note is devoted to several results about frequency localized functions and associated Bernstein inequalities for higher order operators. In particular, we construct some counterexamples for the frequency-localized Bernstein inequalities for higher order Laplacians. We show also that the heat semi-group associated to powers larger than one of the laplacian does not satisfy the strict maximum principle in general. Finally, in a suitable range we provide several positive results.

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