On the Christoffel function for the generalized Jacobi measures on a quasidisk

TL;DR

This paper derives precise bounds for the Christoffel function associated with measures on Jordan domains bounded by quasiconformal curves, emphasizing the importance of boundary quasiconformality.

Contribution

It establishes exact inequalities for the Christoffel function on quasiconformal boundaries, highlighting the necessity of boundary quasiconformality for these bounds.

Findings

Exact double inequality for Christoffel function established

Quasiconformality of boundary is essential for the bounds

Results apply to measures supported on Jordan domains

Abstract

We establish the exact (up to the constants) double inequality for the Christoffel function for a measure supported on a Jordan domain bounded by a quasiconformal curve. We show that this quasiconformality of the boundary cannot be omitted.