Polynomial interpolation and Marcinkiewicz-Zygmund inequalities on the unit circle

The objective of this paper is to derive an intimate relationship among thr ee important mathematical tools, namely: polynomial interpolation, Marcinki ewicz-Zygmund inequalities, and A(p)-weights. In particular, it is shown th at minimum separation of sample points on the unit circle together with cer tain uniform A(p)-weights generated by these sample points constitute a nec essary and sufficient condition for the validity of the Marcinkiewicz-Zygmu nd inequality evaluated at these points, which in turn, is equivalent to th e Jackson-type estimate, using the Popov-Andreev module of continuity, of p olynomial interpolation, again at these Sample points. (C) 1999 Academic Pr ess.