On the sharp Jackson-Nikol'skii inequality for algebraic polynomials on a multidimensional Euclidean sphere
Jackson-Nikol'skii inequalities and their constants are considered in this article for different dimensions \(m\) and polynomial degrees \(n\). Here, \(n\) is the total degree of a polynomial in \(m\) variables. Uniform and \(L^1\)-norms of such polynomials are compared by these estimates, and the central question is the dependence of the best possible constants in the inequalities on \(m\) and \(n\). These are estimated from above and below by multiples of \(n^{m-1}\).
scientific article; zbMATH DE number 5966562