Approximation by rational functions
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- by Ronald A. DeVore PDF
- Proc. Amer. Math. Soc. 98 (1986), 601-604 Request permission
Abstract:
Making use of the Hardy-Littlewood maximal function, we give a new proof of the following theorem of Pekarski: If $fâ$ is in $L\log L$ on a finite interval, then $f$ can be approximated in the uniform norm by rational functions of degree $n$ to an error $O(1/n)$ on that interval.References
- Colin Bennett and Robert Sharpley, Weak-type inequalities for $H^{p}$ and BMO, Harmonic analysis in Euclidean spaces (Proc. Sympos. Pure Math., Williams Coll., Williamstown, Mass., 1978) Proc. Sympos. Pure Math., XXXV, Part, Amer. Math. Soc., Providence, R.I., 1979, pp. 201â229. MR 545259
- Ronald A. DeVore, Maximal functions and their application to rational approximation, Second Edmonton conference on approximation theory (Edmonton, Alta., 1982) CMS Conf. Proc., vol. 3, Amer. Math. Soc., Providence, RI, 1983, pp. 143â155. MR 729327 D. J. Neweman, Rational approximation to $|x|$, Michigan Math. J. 11 (1964), 11-14. A. A. Pekarski, Rational approximation of absolutely continuous functions with derivatives in an Orlicz space, Math. Sb. 45 (1983), 121-137.
- V. A. Popov, On the connection between rational uniform approximation and polynomial $L_{p}$ approximation of functions, Quantitative approximation (Proc. Internat. Sympos., Bonn, 1979) Academic Press, New York-London, 1980, pp. 267â277. MR 588187
Additional Information
- © Copyright 1986 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 98 (1986), 601-604
- MSC: Primary 41A20; Secondary 41A25, 41A63, 42B25
- DOI: https://doi.org/10.1090/S0002-9939-1986-0861758-3
- MathSciNet review: 861758