Geodesic
Conjugate functions and their connection with uniform rational and piecewise-polynomial approximations
Sbornik. Mathematics, Tome 206 (2015) no. 2, pp. 333-340

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As is well known, there is a close relationship between rational and piecewise-polynomial approximations of functions. This relationship is manifested in the most vivid way in the case of approximations in Lebesgue spaces $L_p$ for $0$, $1/p\notin\mathbb N$. In the present paper, in particular, it is shown that the rate of uniform rational approximation of functions is described rather well using the rate of uniform piecewise-polynomial approximations of the function itself and its conjugate function. The converse is also true. Bibliography: 14 titles.
Keywords: conjugate functions, best rational approximations, best piecewise-polynomial approximations
Mots-clés : Besov space. 
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A. A. Pekarskii. Conjugate functions and their connection with uniform rational and piecewise-polynomial approximations. Sbornik. Mathematics, Tome 206 (2015) no. 2, pp. 333-340. http://geodesic.mathdoc.fr/item/SM_2015_206_2_a7/