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Polynomial approximation inL p(S) forp>0
Authors:Z. Ditzian
Affiliation:1. Department of Mathematical Sciences, University of Alberta, T6G 2G1, Edmonton, Alberta, Canada
Abstract:For a simple polytopeS inR d andp>0 we show that the best polynomial approximationE n(f)p≡En(f)Lp(S) satisfies $$E_n left( f right)_p leqslant Comega _S^r left( {f,frac{1}{n}} right)p,$$ where ω S r is a measure of smoothness off. This result is the best possible in the sense that a weak-type converse inequality is shown and a realization of ω S r (f,t)p via polynomial approximation is proved.
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