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Bounds on the derivatives of polynomials on Banach spaces

Published online by Cambridge University Press:  24 October 2008

Yannis Sarantopoulos
Yannis Sarantopoulos
Affiliation:
Department of Mathematical Sciences, Kent State University, Kent, Ohio 44242, U.S.A.
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Abstract

We generalize the classical Bernstein's and Markov's Inequalities for polynomials on any real Banach space. We also give estimates for the derivatives of homogeneous polynomials on real Banach spaces.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 110 , Issue 2 , September 1991 , pp. 307 - 312
Copyright
Copyright © Cambridge Philosophical Society 1991

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References

REFERENCES

[1]Harris, L. A.. Bounds on the derivatives of holomorphic functions of vectors. In Collogue d'analyse (Hermann, 1975), pp. 145–163.Google Scholar
[2]Kellogg, O. D.. On bounded polynomials in several variables. Math. Z. 27 (1928), 55–64.CrossRefGoogle Scholar
[3]Lorentz, G. G.. Approximation of Functions (Holt, Rinehart and Winston, 1966).Google Scholar
[4]Sarantopoulos, I.. Estimates for polynomial norms on Lp(μ) spaces. Math. Proc. Cambridge Philos. Soc. 99 (1986), 263–271.CrossRefGoogle Scholar
[5] The Scottish Book ‘Mathematics from the Scottish Café’, ed. Mauldin, R. D. (Birkhäuser, 1981).Google Scholar
[6]Wilhelmsen, D. R.. A Markov Inequality in several dimensions. J. Approx. Theory 11 (1974), 216–220.CrossRefGoogle Scholar