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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Approximation by rational functions


Author: Ronald A. DeVore
Journal: Proc. Amer. Math. Soc. 98 (1986), 601-604
MSC: Primary 41A20; Secondary 41A25, 41A63, 42B25
MathSciNet review: 861758
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Abstract: Making use of the Hardy-Littlewood maximal function, we give a new proof of the following theorem of Pekarski: If $ f'$ 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 [Enhancements On Off] (What's this?)

  • [1] 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. 201–229. MR 545259 (80j:46044)
  • [2] 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. 143–155. MR 729327 (85g:41022)
  • [3] D. J. Neweman, Rational approximation to $ \vert x\vert$, Michigan Math. J. 11 (1964), 11-14.
  • [4] A. A. Pekarski, Rational approximation of absolutely continuous functions with derivatives in an Orlicz space, Math. Sb. 45 (1983), 121-137.
  • [5] 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. 267–277. MR 588187 (81j:41025)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1986-0861758-3
PII: S 0002-9939(1986)0861758-3
Article copyright: © Copyright 1986 American Mathematical Society