On the summability method of Abel–Poisson type for multiple Fourier integrals

The author examines a class of summability methods for multiple Fourier integrals which contains for certain values of the parameter the Abel–Poisson and Gauss–Weierstrass methods. The properties of the kernels of these methods are studied. A subclass of positive kernels is exhibited. Using the properties established for the kernels, he proves the convergence of the integral means under consideration almost everywhere and in the metric of $L_p$, as well as the existence of a localization principle.
Bibliography: 18 titles.