Upper estimates of Christoffel function on convex domains.

New upper bounds on the pointwise behavior of Christoffel function on convex domains in R d are obtained. These estimates are established by explicitly constructing the corresponding “needle”-like algebraic polynomials having small integral norm on the domain, and are stated in terms of few easy-to-measure geometric characteristics of the location of the point of interest in the domain. Sharpness of the results is shown and examples of applications are given. [ABSTRACT FROM AUTHOR]