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An extension of Bernstein inequality
Journal of Mathematical Analysis and Applications ( IF 1.3 ) Pub Date : 2021-05-03 , DOI: 10.1016/j.jmaa.2021.125289 Ha Huy Bang , Vu Nhat Huy
中文翻译:
伯恩斯坦不等式的扩展
更新日期:2021-05-14
Journal of Mathematical Analysis and Applications ( IF 1.3 ) Pub Date : 2021-05-03 , DOI: 10.1016/j.jmaa.2021.125289 Ha Huy Bang , Vu Nhat Huy
In this paper, we obtain the following extension of Bernstein inequality for polynomial differential operators: if , K is an arbitrary compact set in and is a polynomial, then there exists a constant C such that for all and all , where and is the Fourier transform of f. Further, we use Nikolskii's idea to get Bernstein inequality for polynomial differential operators with different metrics. The corresponding results for polynomial integral operators are given. An application is also given.
中文翻译:
伯恩斯坦不等式的扩展
在本文中,对于多项式微分算子,我们得到了Bernstein不等式的以下扩展: ,K是在 和 是多项式,那么存在一个常数C使得 对所有人 和所有 , 在哪里 和 是f的傅立叶变换。此外,我们使用Nikolskii的想法来获得具有不同度量的多项式微分算子的Bernstein不等式。给出了多项式积分算子的相应结果。还提供了一个应用程序。