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arXiv · 1602.08545

The Bernstein inequality for slice regular polynomials

Zhenghua Xu
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Abstract

Due to the invalidation of the Gauss-Lucas type result for quaternionic polynomials, we first give in this paper an alternative proof of the Bernstein inequality in $L^{p} (1\leq p \leq+\infty)$ for slice regular polynomials by the Fejér kernel and the Minkowski inequality. Secondly, we extend a result of Ankeny-Rivlin to the quaternionic setting via the Hopf lemma. By the way, some Turan inequalities are established for slice regular polynomials.

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Zhenghua Xu. 2019-04-23. The Bernstein inequality for slice regular polynomials. https://doi.org/10.1007/s11785-019-00919-w

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