Singular Integral Operators in Spaces of Oscillating Functions on a Rectifiable Curve
We prove generalized Noether theorems for a singular integral equation with Cauchy kernel on a closed rectifiable Jordan curve in classes of piecewise-continuous functions with oscillation-type discontinuities. We obtain results concerning the normal solvability of operators associated with the equation and acting into a Banach space and incomplete normed spaces of piecewise-continuous oscillating functions.
English version (Springer): Ukrainian Mathematical Journal 55 (2003), no. 9, pp 1457-1471.
Citation Example: Plaksa S. A. Singular Integral Operators in Spaces of Oscillating Functions on a Rectifiable Curve // Ukr. Mat. Zh. - 2003. - 55, № 9. - pp. 1206-1217.