International Journal of Mathematics and Mathematical Sciences
Volume 14 (1991), Issue 4, Pages 625-638

Finite-infinite range inequalities in the complex plane

H. N. Mhaskar

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 EC be closed, ω be a suitable weight function on E, σ be a positive Borel measure on E. We discuss the conditions on ω and σ which ensure the existence of a fixed compact subset K of E with the following property. For any p, 0<P, there exist positive constants c1, c2 depending only on E, ω, σ and p such that for every integer n1 and every polynomial P of degree at most n, E\K|ωnP|pdσc1exp(c2n)K|ωnP|pdσ. In particular, we shall show that the support of a certain extremal measure is, in some sense, the smallest set K which works. The conditions on σ are formulated in terms of certain localized Christoffel functions related to σ.