Advanced Mathematical Models & Applications

In this paper, we investigate questions about the nontangential convergence of certain singular integrals of the convolution type. We estimate the rate of approximation of locally summable functions by singular integrals in terms of metric characteristics describing the structural properties of the locally summable function. Here we can talk, for example about the existence of nontangential limit of the Possion integral, the Gauss-Weierstrass integral and others, and also harmonic functions of many variables. The issue of nontangential convergence (i.e. convergence in the interior of some angle) of singular integrals is of great scientific interest. Therewith, estimation of the approximation rate of a locally summable function by means of singular integrals, whose density is this function, is of great importance.