Approximation by rational functions

Author:
Ronald A. DeVore

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

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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 is in on a finite interval, then can be approximated in the uniform norm by rational functions of degree to an error on that interval.

**[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****[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****[3]**D. J. Neweman,*Rational approximation to*, 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**

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DOI:
https://doi.org/10.1090/S0002-9939-1986-0861758-3

Article copyright:
© Copyright 1986
American Mathematical Society