Maximal Sets of Convergence and Unbounded Divergence of Multiple Fourier Series with J_k-Lacunary Sequence of Partial Sums

摘要

We study the behavior of the rectangular partial sums S_n(x; f) of a multiple trigonometric Fourier series of a function rnf∈L_p(T~N), p≥1, where T~N = (-π, π)~N, N ≥ 3,rnas n → ∞ (i.e., min_(1≤1j≤N)n_j → ∞) for the case in which some of the components n_j of the vector n = (n_1, n_2, ... ,n_N) are elements of (one-dimensional) lacunary sequences. Let us proceed to precise statements.