Suppose C C RN is a closed convex bounded body containing 0 in its interior. If əC is sufficiently smooth with strictly positive Gauss curvature at each point, then, denoting by Lr c the Lebesgue constant relative to C, there exists a constant A > 0 such that Lr c≥ Ar(N-l)/2 for r sufficiently large. This complements the known result that there exists a constant B such that Lr c ≤ Br(N-l)/2 for r sufficiently large
Carenini, M., Soardi, P. (1983). Sharp estimates for Lebesgue constants. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 89(3), 449-452 [10.1090/S0002-9939-1983-0715864-1].
Sharp estimates for Lebesgue constants
SOARDI, PAOLO MAURIZIO
1983
Abstract
Suppose C C RN is a closed convex bounded body containing 0 in its interior. If əC is sufficiently smooth with strictly positive Gauss curvature at each point, then, denoting by Lr c the Lebesgue constant relative to C, there exists a constant A > 0 such that Lr c≥ Ar(N-l)/2 for r sufficiently large. This complements the known result that there exists a constant B such that Lr c ≤ Br(N-l)/2 for r sufficiently large
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