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Proceedings of the American Mathematical Society

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Sharp estimates for Lebesgue constants

Authors: Marco Carenini and Paolo M. Soardi
Journal: Proc. Amer. Math. Soc. 89 (1983), 449-452
MSC: Primary 42B05
MathSciNet review: 715864
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Abstract: Suppose $ C \subset {R^N}$ is a closed convex bounded body containing 0 in its interior. If $ \partial C$ is sufficiently smooth with strictly positive Gauss curvature at each point, then, denoting by $ {L_{r,C}}$ the Lebesgue constant relative to $ C$, there exists a constant $ A > 0$ such that $ {L_{r,C}} \geqslant A{r^{(N - 1)/2}}$ for $ r$ sufficiently large. This complements the known result that there exists a constant $ B$ such that $ {L_{r,C}} \leqslant B{r^{(N - 1)/2}}$ for $ r$ sufficiently large.

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