On asymptotical expansions for certain singular integrals: 2-dimensional case

One discusses a problem of asymptotical behavior for some operators in a general theory of pseudo differential equations on manifolds with borders. Using the distribution theory one obtains certain explicit representations for these operators. These limit distributions are constructed with a help of the Fourier transform, Dirac mass-function and its derivatives, and well-known distribution related to the Cauchy type integral.