Markov-Bernstein-type inequality for trigonometric polynomials with respect to doubling weights on [-omega,omega] Academic Article

abstract

• Various important, weighted polynomial inequalities, such as Bernstein, Marcinkiewicz, Nikolskii, Schur, Remez, etc., have been proved recently by Giuseppe Mastroianni and Vilmos Totik under minimal assumptions on the weights. In most cases this minimal assumption is the doubling condition. Here, based on a recently proved Bernstein-type inequality by D. S. Lubinsky, we establish Markov-Bernstein-type inequalities for trigonometric polynomials with respect to doubling weights on [-, ]. Namely, we show the theorem below.

authors

• Erdelyi, Tamas

published proceedings

• CONSTRUCTIVE APPROXIMATION

author list (cited authors)

• Erdelyi, T.

citation count

• 9

complete list of authors

• Erdelyi, T

publication date

• March 2003

publisher

• Springer Nature  Publisher

published in

• Constructive Approximation  Journal

keywords

• Doubling Weights
• Markov-bernstein Inequality
• Trigonometric Polynomials
• Videnskii's Inequality

Digital Object Identifier (DOI)

• 10.1007/s00365-002-0504-3

start page

• 329

end page

• 338

volume

• 19

issue

• 3

URL

• http%3A%2F%2Fdx.doi.org%2F10.1007%2Fs00365-002-0504-3

user-defined tag

• 10 Reduced Inequalities