U-convergence of multiple Fourier series

摘要

The u-convergencs of rmiltiple Fourier series is studied, generalizing convergence in the Pringsheim. sense, with respect to spheres. A definitive condition in terms, of moduli of smoothness is found on a functional class that implies the it-convergence of Fourier series in the metrics Lp(Tm), where l≤p≤oo,p≠2 and m≥2.