Generalized Cauchy Integrals on the Plane

Viktor Polunin, Alexandre Soldatov


The integrals with homogeneous - difference kernels are considered on a smooth contour.
The boundary properties of the integrals are described in the H\"{o}lder space.
An analogue of the known Sokhotski -- Plemelj formula is received. Nevertheless the
differentiation formula of these integrals is also given.

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