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

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arxiv 2109.07952 v1 pith:6EDNU7I2 submitted 2021-09-16 math.AP math.FA

Dong Li , Yannick Sire This is my paper · ORCID
classification math.APmath.FA
keywords bernsteinhigherorderresultsassociatedinequalitiesoperatorsseveral
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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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