The Cauchy integral over non-rectifiable paths

Interactions of germs with applications

“…There exist publications dealing with this subject . The present paper continues the work , but unlike the last one, we define the generalized integration as interaction of germs with supports on non‐rectifiable curves (in , it is defined as distribution).…”

Cauchy integral and singular integral operator over closed Jordan curves

“…It is enough to assume them to be of bounded generalized variation (see, for instance, [29]). In this connection, the definition of -rectifiable curves given in [24,26] follows Let (x) be an increasing function defined for…”

Integration over non-rectifiable curves and Riemann boundary value problems

“…as definition of its left side for non-rectifiable curve Γ of null planar Lebesgue measure (see, for instance, [11,15] and references in [16]). For an 1-form ω equals to f (t) dt, this definition turns into…”