Geodesic
Conjugate Functions on the Closed Interval and Their Relationship with Uniform Rational and Piecewise Polynomial Approximations
Matematičeskie zametki, Tome 99 (2016) no. 2, pp. 248-261

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Earlier the second author showed that, in the periodic case, the rate of best uniform rational approximations of a function is well described in terms of the rates of best uniform piecewise polynomial approximations of the function itself and its conjugate. In the present paper, a similar result is obtained for a closed interval.
Keywords: best uniform rational approximation of a function, best uniform piecewise polynomial approximation, $L_p$-modulus of smoothness, Jordan curve, Szegö-type inequality.
Mots-clés : Besov space $B_p^\alpha$ 
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     author = {T. S. Mardvilko and A. A. Pekarskii},
     title = {Conjugate {Functions} on the {Closed} {Interval} and {Their} {Relationship} with {Uniform} {Rational} and {Piecewise} {Polynomial} {Approximations}},
     journal = {Matemati\v{c}eskie zametki},
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T. S. Mardvilko; A. A. Pekarskii. Conjugate Functions on the Closed Interval and Their Relationship with Uniform Rational and Piecewise Polynomial Approximations. Matematičeskie zametki, Tome 99 (2016) no. 2, pp. 248-261. http://geodesic.mathdoc.fr/item/MZM_2016_99_2_a7/