V. V. Arestov, V. N. Gabushin, “Approximation of classes of differentiable functions”, Mat. Zametki, 1971, Volume 9, Issue 2,Pages <nobr>105

This article is cited in 4 papers

Approximation of classes of differentiable functions

V. V. Arestov, V. N. Gabushin

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

Abstract: Conditions are derived under which
$$ F=\sup_{||f^{(k)}||_{L_p(S)}\leqslant1}\,\inf_{||\varphi^{(l)}||_{L_r(S)}\leqslant n}||f-\varphi||_{L_p(S)} $$
is finite or infinite. The value of $F$ is calculated for certain special cases.

UDC: 517.5

Received: 02.03.1970