Abstract

The paper proves that, if f(x) ∈ L[−1,1]p, 1 ≤ p < ∞, changes sign l times in (−1, 1), then there exists a real rational function r(x) ∈ Rn(2μ−1)l which is copositive with f(x), such that the following Jackson type estimate $$ \left\| {f - r} \right\|_p \leqslant C_\delta l^{2\mu } \omega _\rho \left( {f,\frac{1} {n}} \right)_p $$ holds, where μ is a natural number ≥ 3/2 + 1/p, and Cδ is a positive constant depending only on δ.

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