Pólya-Type Polynomial Inequalities in L^P Spaces and Best Local Approximation

ABSTRACT

In this paper, we obtain an extension of the Pólya inequality for univariate real polynomials in L ^p spaces and new estimates for certain class of measurable sets. Inequalities for complex polynomials are also considered. We give an application to a multipoint best local approximation problem for real and complex polynomials.

Keywords:

• Algebraic polynomials
• Best local approximation
• Pólya-type inequalities

Mathematics Subject Classification:

• Primary 41A17
• Secondary 26D07

ACKNOWLEDGMENT

This work was supported by Universidad Nacional de Rio Cuarto and Conicet.