We considered a kind of singular integral operator with Weierstrass function kernel on a simple closed smooth curve in a fundamental period parallelogram. Using the method of complex functions, we established the Bertrand Poincaré formula for changing order of the corresponding integration, and some important properties for this kind of singular integral operator.
M. C. De Bonis and C. Laurita, “Numerical Solution of Systems of Cauchy Singular Integral Equations with Con stant Coefficients,” Applied Mathematics and Computa tion, Vol. 219, No. 4, 2012, pp. 1391-1410.