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Bernstein and Markov-type inequalities for polynomials on real Banach spaces

Published online by Cambridge University Press:  06 November 2002

GUSTAVO A. MUÑOZ  and
YANNIS SARANTOPOULOS
GUSTAVO A. MUÑOZ
Affiliation:
Facultad de Matemáticas, Departamento de Análisis, Universidad Complutense de Madrid, Madrid 28040, Spain. e-mail: gustavo@sunam1.mat.ucm.es
YANNIS SARANTOPOULOS
Affiliation:
Mathematics Department, National Technical University, Zografou Campus 157 80, Athens, Greece. e-mail: ysarant@math.ntua.gr
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Abstract

In this work we generalize Markov's inequality for any derivative of a polynomial on a real Hilbert space and provide estimates for the second and third derivatives of a polynomial on a real Banach space. Our result on a real Hilbert space answers a question raised by L. A. Harris in his commentary on problem 74 in the Scottish Book [20]. We also provide generalizations of previously obtained inequalities of the Bernstein and Markov-type for polynomials with curved majorants on a real Hilbert space.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 133 , Issue 3 , November 2002 , pp. 515 - 530
Copyright
© 2002 Cambridge Philosophical Society

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