International Journal of Mathematics and Mathematical Sciences
Volume 14 (1991), Issue 4, Pages 625-638
Finite-infinite range inequalities in the complex plane
Department of Mathematics, California State University, Los Angeles 90032, California, USA
Received 23 April 1990
Copyright © 1991 H. N. Mhaskar. 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.
Let be closed, be a suitable weight function on , be a positive
Borel measure on . We discuss the conditions on and which ensure the existence of
a fixed compact subset of with the following property. For any , , there
exist positive constants depending only on , , and such that for every integer
and every polynomial of degree at most ,
In particular, we shall show that the support of a certain extremal measure is, in some
sense, the smallest set which works. The conditions on are formulated in terms of
certain localized Christoffel functions related to .