关于高阶算子Bernstein不等式及相关结果的注记
Remarks on the Bernstein inequality for higher order operators and related results
摘要：
本文主要讨论高阶算子的频率局部化函数及其Bernstein不等式的若干结果。特别地，我们构造了高阶拉普拉斯算子的频率局部化Bernstein不等式的反例。我们还证明了幂次大于拉普拉斯算子的热半群一般不满足严格的最大值原理。最后，在适当的范围内，我们提供了一些积极的结果。
英文摘要：
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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