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arXiv · 2109.07952

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

Dong Li·Yannick Sire
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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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Dong Li, Yannick Sire. 2021-09-16. Remarks on the Bernstein inequality for higher order operators and related results. https://arxiv.org/abs/2109.07952

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