Approximation by rational functions
Author:
Ronald A. DeVore
Journal:
Proc. Amer. Math. Soc. 98 (1986), 601604
MSC:
Primary 41A20; Secondary 41A25, 41A63, 42B25
MathSciNet review:
861758
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Abstract 
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Abstract: Making use of the HardyLittlewood 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, Weaktype 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 , Michigan Math. J. 11 (1964), 1114.
 [4]
A. A. Pekarski, Rational approximation of absolutely continuous functions with derivatives in an Orlicz space, Math. Sb. 45 (1983), 121137.
 [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 YorkLondon, 1980, pp. 267–277. MR 588187
(81j:41025)
 [1]
 C. Bennett and R. Sharpley, Weak type inequalities for and BMO, Harmonic Analysis in Euclidean Spaces, Proc. Sympos. Pure Math., vol. 35, Amer. Math. Soc., Providence, R.I., 1979, pp. 201229. MR 545259 (80j:46044)
 [2]
 R. DeVore, Maximal functions and their application to rational approximation, Approximation Theory, CMS Conf. Proc., vol. 3, Amer. Math Soc., Providence, R.I., 1983, pp. 143155. MR 729327 (85g:41022)
 [3]
 D. J. Neweman, Rational approximation to , Michigan Math. J. 11 (1964), 1114.
 [4]
 A. A. Pekarski, Rational approximation of absolutely continuous functions with derivatives in an Orlicz space, Math. Sb. 45 (1983), 121137.
 [5]
 V. Popov, On the connection between rational uniform approximation and polynomial approximation of functions, Quantitative Approximation, Academic Press, New York, 1980, pp. 119129. MR 588187 (81j:41025)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939198608617583
PII:
S 00029939(1986)08617583
Article copyright:
© Copyright 1986
American Mathematical Society
