On the mean convergence of multiple Fourier series and the asymptotics of the Dirichlet kernel of spherical means

Preprint no. 52 (1971), Institut Prikladnoi Matematiki Akademii Nauk USSR, Moscow (in Russian). Translated into English by E. Liflyand. See comments to this paper by E. Liflyand in this volume of the Eurasian Mathematical Journal.