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

TitleBernstein and Markov-type inequalities for polynomials on Lp(μ) spaces
Publication TypeJournal Article
Year of Publication2019
AuthorsChatzakou, M, Sarantopoulos, Y
JournalDolomites Research Notes on Approximation
Volume12
IssueSpecial_Issue
Pagination16-28
Date Published10/2019
PublisherPadova University Press
Place PublishedPadova, IT
ISSN Number2035-6803
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 Lp(μ) spaces. We also give applications to homogeneous polynomials and symmetric multilinear mappings in Lp(μ) spaces. Finally, Bernstein’s inequality for homogeneous polynomials on both real and complex Hilbert spaces has been discussed.