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

Full-text PDF

Abstract | References | Similar Articles | Additional Information

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]**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. 201-229. 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. 143-155. MR**729327 (85g:41022)****[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. Popov,*On the connection between rational uniform approximation and polynomial**approximation of functions*, Quantitative Approximation, Academic Press, New York, 1980, pp. 119-129. MR**588187 (81j:41025)**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
41A20,
41A25,
41A63,
42B25

Retrieve articles in all journals with MSC: 41A20, 41A25, 41A63, 42B25

Additional Information

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

Article copyright:
© Copyright 1986
American Mathematical Society