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- W309030724 abstract "Nikol’skii inequalities for various sets of functions, domains, and weights will be discussed. Much of the work is dedicated to the class of algebraic polynomials of total degree n on a bounded convex domain D. That is, we study $$sigma := sigma (D,d)$$ for which $$begin{aligned} Vert PVert _{L_q(D)}le c n^{sigma (frac{1}{p}-frac{1}{q})}Vert PVert _{L_p(D)},quad 0<ple qle infty , end{aligned}$$ where P is a polynomial of total degree n. We use geometric properties of the boundary of D to determine $$sigma (D,d)$$ with the aid of comparison between domains. Computing the asymptotics of the Christoffel function of various domains is crucial in our investigation. The methods will be illustrated by the numerous examples in which the optimal $$sigma (D,d)$$ will be computed explicitly." @default.
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- W309030724 date "2016-04-15" @default.
- W309030724 modified "2023-09-25" @default.
- W309030724 title "On Nikol’skii Inequalities for Domains in $${mathbb {R}}^d$$ R d" @default.
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- W309030724 doi "https://doi.org/10.1007/s00365-016-9335-5" @default.
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