Polynomial Interpolation and Marcinkiewicz-Zygmund Inequalities on the Unit CircleU

The objective of this paper is to derive an intimate relationship among three important mathematical tools, namely: polynomial interpolation, Marcinkiewicz- Zygmund inequalities, and Ap-weights. In particular, it is shown that minimum separation of sample points on the unit circle together with certain uniform Ap-weights generated by these sample points constitute a necessary and sufficient condition for the validity of the Marcinkiewicz-Zygmund inequality evaluated at these points, which in turn, is equivalent to the Jackson-type estimate, using the Popov-Andreev module of continuity, of polynomial interpolation, again at these sample points.