Abstract
Let f : R → R have an nth derivative of finite variation V f ( n ) and a locally absolutely continuous ( n - 1 ) st derivative. Denote by E ± ( δ , f ) p the error of onesided approximation of f (from above and below, respectively) by entire functions of exponential type δ > 0 in L p ( R ) -norm. For 1 ≤ p ≤ ∞ we show the estimate E ± ( δ , f ) p ⩽ C n 1 - 1 / p π 1 / p V f ( n ) δ - n - 1 p , with constants C n > 0 .
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