Arestov's theorems on Bernstein's inequality Academic Article

abstract

• We give a simple, elementary, and at least partially new proof of Arestov's famous extension of Bernstein's inequality in $L_p$ to all $p geq 0$. Our crucial observation is that Boyd's approach to prove Mahler's inequality for algebraic polynomials $P_n in {mathcal P}_n^c$ can be extended to all trigonometric polynomials $T_n in {mathcal T}_n^c$.

authors

• Erdelyi, Tamas

published proceedings

• JOURNAL OF APPROXIMATION THEORY

author list (cited authors)

• Erdelyi, T.

citation count

• 4

complete list of authors

• Erdelyi, Tamas

publication date

• February 2020

publisher

• Elsevier  Publisher

published in

• Journal of Approximation Theory  Journal

keywords

• Arestov's Theorem
• Bernstein's Inequality In L-p For All P >= 0

Digital Object Identifier (DOI)

• 10.1016/j.jat.2019.105323

start page

• 105323

end page

• 105323

volume

• 250

URL

• http://dx.doi.org/10.1016/j.jat.2019.105323

user-defined tag

• 10 Reduced Inequalities