The authors give alternative proofs for k=1 and 2, establish the sharp constant and optimal kernel for k=3, handle restricted cases for k=4 and 6 with non-negative Fourier transforms, and relate the constants for ∇^k and ∇^{2k}.
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The smoothest average and some extremal problems for polynomials
The authors give alternative proofs for k=1 and 2, establish the sharp constant and optimal kernel for k=3, handle restricted cases for k=4 and 6 with non-negative Fourier transforms, and relate the constants for ∇^k and ∇^{2k}.