Copyright © 2009 Feilong Cao and Shaobo Lin. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Essentially sharp Markov-type inequalities are known for various
classes of polynomials with constraints including constraints of the coefficients of
the polynomials. For and we introduce the class as the collection of
all polynomials of the form , , , . In this paper, we prove essentially sharp Markov-type inequalities for polynomials
from the classes on . Our main result shows that the Markov factor valid for all polynomials of degree at most on improves to for polynomials in the classes on .