Bernstein and Markov-type inequalities for polynomials on L_p(μ) spaces

2020/03/24 by M. Chatzakou, Y. Sarantopoulos · 1 citation
Mathematics · #math.FA

paper · pdf · doi:10.14658/pupj-drna-2019-special_issue-4

published as Dolomites Research Notes on Approximation, Volume 12, 2019, 16-28

arxiv created 2020/03/24 · arxiv updated 2020/03/25

Abstract

In this work, we discuss generalizations of the classical Bernstein and Markov type inequalities for polynomials and we present some new inequalities for the kth Fréchet derivative of homogeneous polynomials on real and complex L_p(μ) spaces. We also give applications to homogeneous polynomials and symmetric multilinear mappings in L_p(μ) spaces. Finally, Bernstein's inequality for homogeneous polynomials on both real and complex Hilbert spaces has been discussed.

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