Volume 25, pp. 278-283, 2006.

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)|1 for every xKE, 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 Rd.

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Key words

Remez-type inequalities, homogeneous polynomials

AMS subject classifications

41A17