On the convergence of Riesz spherical means of multiple Fourier series and integrals of functions of bounded generalized variation

A necessary and sufficient condition is found for the pointwise convergence of the Riesz spherical means of critical order of multiple Fourier series and integrals in the class of functions whose spherical Steklov means at the given point have (as a function of the radius of the sphere) bounded generalized variation.
Bibliography: 25 titles.