Whitney Estimates for Convex Domains with Applications to Multivariate Piecewise Polynomial Approximation
نویسندگان
چکیده
منابع مشابه
Whitney Estimates for Convex Domains with Applications to Multivariate Piecewise Polynomial Approximation
We prove the following Whitney estimate. Given 0 < p ≤ ∞, r ∈ N, and d ≥ 1, there exists a constant C(d, r, p), depending only on the three parameters, such that for every bounded convex domain ⊂ Rd , and each function f ∈ L p( ), Er−1( f, )p ≤ C(d, r, p)ωr ( f, diam( ))p, where Er−1( f, )p is the degree of approximation by polynomials of total degree, r − 1, and ωr ( f, ·)p is the modulus of s...
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ژورنال
عنوان ژورنال: Foundations of Computational Mathematics
سال: 2004
ISSN: 1615-3375,1615-3383
DOI: 10.1007/s10208-004-0096-3