Behavior of the Singular Integral Along the Real Axis with the Density Vanishing at Infinity Near Infinity

We study the behavior of singular integral along the real axis in the neighborhood of the point at infinity, when its density satisfy Hölder condition in any finite part of the real axis and is continuous function in the neighborhood of the point at infinity, which decreases with the order of decreasing same as the lower then the minus first power of logarithm of the absolute value of the coordinate of the point of the real axis, when we move this point unlimitedly from the origin.