On boundary values for rectifiable curves of a generalization of the Cauchy-type integral related to the Helmholtz operator in $R^2$

摘要

There are considered vector fields and quaternionic $\alpha$-hyperholomorphicfunctions in a domain of $R^2$ which generalize the notion of solenoidal andirrotational vector fields. There are established sufficient conditions for thecorresponding Cauchy-type integral along a closed Jordan rectifiable curve tobe continuously extended onto the closure of a domain. TheSokhotski-Plemelj-type formulas are proved as well.