Metric dimensions, generalized integrations, Cauchy transform, and Riemann boundary-value problem on nonrectifiable arcs (Q357259)

Introducing certain distributions with supports on non-rectifiable arcs, which generalize the weighted integration along this arc, the author studies the boundary behaviour of the Cauchy transforms of theses distributions. The present paper is devoted to a description of the solutions of the Riemann boundary value problems in terms of a new version of the metric dimension of a non-rectifiable arc.