Title: Upper estimates of Christoffel function on convex domains,
Abstract: New upper bounds on the pointwise behaviour of Christoffel function on convex
domains in ${\mathbb{R}}^d$ 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.