Analytic and geometric quasiinvariants of convex curvelinear polygons with infinite number of vertices

Establishing and evaluation of values of the basic curvelinear quasiinvariants of Jordan curves still remains an important problem of geometric and quasiconformal analysis, especially for applications. It is not solved completely even for polygonal domains. The most general known results were established for unbounded polygons with locally smooth boundaries containing the infinite point and having only a finite number of vertices.

The present paper deals with convex polygonal domains having infinite (countable) number of vertices. It creates a new approach in this direction and establishes that quasiinvariants of such polygons are estimated by their geometric characteristics.