The present paper discusses in the metric S. N. Bernstein type inequalities of the most general kind on very general accessible classes of curves in a complex plane. The obtained estimations, generally speaking, are not improvable.
"S. N. Bernstein Type Estimations in the Mean on the Curves in a Complex Plane." Abstr. Appl. Anal. 2009 1 - 19, 2009. https://doi.org/10.1155/2009/165194