Approximation by Reciprocals of Polynomials with Positive Coefficients in L p Spaces期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Approximation by Reciprocals of Polynomials with Positive Coefficients in L p Spaces

Authors:	Y. Zhau S.P. Zhou

Affiliation:	(1) The Mathematical Institute, Ningbo University, Ningbo, Zhejiang, 315211, China;(2) Department of Mathematics, Zhejiang University, Hangzhou, Zhejiang, 310028, China

Abstract:	We prove that, if f(x) L^p_[0,1], 1 < p < , f(x) 0, x [0,1], f 0, then there is a polynomial p(x) ⁺_n such that f - 1/p_LP C(p)(f,n^-1/2)_LP where ⁺_n indicates the set of all polynomials of degree n with positive coeficients (see the definition (1) in the text).

Keywords:	reciprocal Jackson type estimate nonnegative function L^p space
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