Abstract:
In this paper, we obtain the structural and geometric characteristics of some subsets of $\mathbb{T}^N=[-\pi,\pi]^N$ (of positive measure), on which, for the classes $L_p(\mathbb{T}^N)$, $p>1$, where $N\ge 3$, weak generalized localization for multiple trigonometric Fourier series is valid almost everywhere, provided that the rectangular partial sums $S_n(x;f)$ ($x\in\mathbb{T}^N$, $f\in L_p$) of these series have a “number” $n=(n_1,\dots,n_N)\in\mathbb Z_{+}^{N}$ such that some components $n_j$ are elements of lacunary sequences. For $N=3$, similar studies are carried out for generalized localization almost everywhere.
Fulltext:
PDF file (618 kB)
