This article is cited in 6 papers

Best approximations in $L_[0,infty)$ of the differentiation operator

V. I. Berdyshev

V. A. Steklov Institute of Mathematics, Sverdlovsk Branch of the Academy of Sciences of USSR

Abstract: A solution of Stechkin's problem concerning the approximation in $L_[0,infty)$ of the first-order differentiation operator in the class of functions of arbitrary bounded variation; the exact constant in the inequality $\|f'\|\leqslant K(\|f\|\bigvee\limits_0^\infty f')^{1/2}$ is found.

UDC: 517.5

Received: 04.05.1970

 English version: Mathematical Notes, 1971, 9:5, 275–277

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