This article is cited in 4 papers

New metric characteristics of non-rectifiable curves with applications

D. B. Kats

Kazan (Volga Region) Federal University, Kazan, Russia

Abstract: In this paper, the author summarizes the concept of Marcinkiewicz exponents, introduced earlier. These exponents are in fact new metric characteristics for non-rectifiable flat curves. The generalization that is presented here is used to solve boundary-value problems for holomorphic functions in domains whose boundaries are non-rectifiable.

Keywords: metric characteristics, fractals, non-rectifiable curves, Marcinkiewicz exponents.

UDC: 517.53/.55

Received: 06.10.2014