## A note on the sharpness of the Remez-type inequality for homogeneous polynomials on the sphere

M. Yattselev

### Abstract

Remez-type inequalities provide upper bounds for the uniform norms of polynomials $p$ on given compact sets $K,$ provided that $|p(x)|\leq1$ for every $x\in K\setminus E,$ where $E$ is a subset of $K$ of small measure. In this note we obtain an asymptotically sharp Remez-type inequality for homogeneous polynomials on the unit sphere in ${\bf R}^d.$

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### Key words

Remez-type inequalities, homogeneous polynomials

41A17

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