부산대학교 도서관

Let $\varepsilon=\{\varepsilon_n\}_{n=1}^\infty$ be a sequence of positive numbers monotonically decreasing to 0, let $C_\varepsilon$ be the set of those $2\pi$-periodic functions whose best approximation by trigonometric polynomials of order $n$ does not exceed $\varepsilon_n\ (n=0,1,\cdots)$, and let $$ V_{n,l}(f,x)=(1/(l+1))\sum_{j=0}^lS_{n+j}(f,x)\quad(n,l=0,1,\cdots), $$ the delayed de la Vallée Poussin means. Then there exist absolute positive constants $c_1$ and $c_2$ such that $$ \multline c_1\sum_{j=n}^{2(n+l)}\frac{\varepsilon_j}{l+j-n+1}\leq\mathop{\sup}\limits_{f\in C_\varepsilon} \mathop{\max}\limits_{-\infty