This article is cited in 10 scientific papers (total in 10 papers)
Rational approximations of absolutely continuous functions with derivative in an Orlicz space
A. A. Pekarskii
Let $R_n(f)$ be the best uniform approximation of $f \in C[0,1]$ by rational fractions of degree at most $n$, and let $ W[0,1]$ be the set of monotone convex functions $w\in C[0,1]$ such that $w(0)=0$ and $w(1)=1$.
Theorem 1. Suppose the function $f$ is absolutely continuous on the interval $[0,1],$
and let $w\in W[0,1]$ and $\widehat f= f(w(x))$.
If $|\widehat f'|\ln^+|\widehat f'|$ is summable on $[0,1],$ then $R_n(f)=o(1/n)$.
Various applications and generalizations of this result are given, and the periodic case is also considered.
Bibliography: 23 titles.
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Mathematics of the USSR-Sbornik, 1983, 45:1, 121–137
MSC: Primary 26A46, 41A20, 46E30; Secondary 41A50
A. A. Pekarskii, “Rational approximations of absolutely continuous functions with derivative in an Orlicz space”, Mat. Sb. (N.S.), 117(159):1 (1982), 114–130; Math. USSR-Sb., 45:1 (1983), 121–137
Citation in format AMSBIB
\paper Rational approximations of absolutely continuous functions with derivative in an Orlicz space
\jour Mat. Sb. (N.S.)
\jour Math. USSR-Sb.
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Starovoitov A., “Rational Approximation of Functions with a Derivative with a Finite Variation”, Dokl. Akad. Nauk Belarusi, 28:2 (1984), 104–106
Devore R., “Approximation by Rational Functions”, Proc. Amer. Math. Soc., 98:4 (1986), 601–604
A. A. Pekarskii, “Tchebycheff rational approximation in the disk, on the circle, and on a closed interval”, Math. USSR-Sb., 61:1 (1988), 87–102
Pekarskii A., “Direct and Inverse-Theorems of the Rational Approximation and Differential Properties of the Functions”, Dokl. Akad. Nauk Belarusi, 31:6 (1987), 500–503
Pekarskii A., “Direct and Converse Theorems of Rational Approximation in the Spaces Lp[-1,1] and C[-1,1]”, 293, no. 6, 1987, 1307–1310
Moskona E., Petrushev P., “Characterization of the Rational Approximation in Uniform Metrics”, 42, no. 2, 1989, 37–40
Moskona E., Petrushey P., “Uniform Rational Approximation of Functions with 1st Derivative in the Real Hardy Space Re H1”, Constr. Approx., 7:1 (1991), 69–103
A. A. Pekarskii, “Uniform rational approximations and Hardy–Sobolev spaces”, Math. Notes, 56:4 (1994), 1082–1088
V. N. Rusak, I. V. Rybachenko, “The Properties of Functions and Approximation by Summation Rational Operators on the Real Axis”, Math. Notes, 76:1 (2004), 103–110
Jafarov S.Z., “Approximation of Conjugate Functions by Trigonometric Polynomials in Weighted Orlicz Spaces”, J. Math. Inequal., 7:2 (2013), 271–281
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