A weighted polynomial inequality

Author:
D. S. Lubinsky

Journal:
Proc. Amer. Math. Soc. **92** (1984), 263-267

MSC:
Primary 41A17; Secondary 26D05, 42C99

MathSciNet review:
754716

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Abstract: In the theory of orthogonal polynomials for weights with noncompact support, much use is made of inequalities relating weighted integrals of polynomials over infinite and finite ranges. Using a short new method of proof, we show such inequalities hold for very general weights in and certain Orlicz spaces.

**[1]**G. A. Baker, Jr.,*Essentials of Podé approximants*, Academic Press, New York, 1975.**[2]**G. Freud,*On two polynomial inequalities. I*, Acta Math. Acad. Sci. Hungar.**22**(1971/1972), 109–116. MR**0288221****[3]**Géza Freud,*On polynomial approximation with respect to general weights*, Functional analysis and its applications (Internat. Conf., Eleventh Anniversary of Matscience, Madras, 1973; dedicated to Alladi Ramakrishnan), Springer, Berlin, 1974, pp. 149–179. Lecture Notes in Math., Vol. 399. MR**0404924****[4]**D. S. Lubinsky,*Estimates of Freud-Christoffel functions for some weights with the whole real line as support*, J. Approx. Theory**44**(1985), no. 4, 343–379. MR**804850**, 10.1016/0021-9045(85)90086-3**[5]**H. N. Mhaskar and E. B. Saff,*Extremal problems for polynomials with exponential weights*, Trans. Amer. Math. Soc.**285**(1984), no. 1, 203–234. MR**748838**, 10.1090/S0002-9947-1984-0748838-0**[6]**R. A. Zalik,*Inequalities for weighted polynomials*, J. Approx. Theory**37**(1983), no. 2, 137–146. MR**690356**, 10.1016/0021-9045(83)90058-8

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1984-0754716-9

Keywords:
Weighted polynomial inequality,
noncompactly supported weight

Article copyright:
© Copyright 1984
American Mathematical Society