On Weyl multipliers of the rearranged trigonometric system

The Square Variation of Rearranged Fourier Series

We prove that there exists a rearrangement of the first $N$ elements of the trigonometric system such that the $L^2$-norm of the square variation operator is at most $O_ε(\log^{9/22+ε}(N))$. This is an improvement over $O(\log^{1/2}(N))$ from the canonical ordering.

关于多重三角系统Weyl乘子的UC乘子

On UC-multipliers for multiple trigonometric systems

研究了能作为所有多重三角系统重排几乎处处收敛Weyl乘子的序列w(n)，证明其必须满足logn≈w(n)≈log²n，并建立了一维与多维三角系统之间的等价原理，可将一维结果推广至高维。

小波型级数绝对收敛性的定量估计

Quantitative estimates for the absolute convergence of wavelet-type series

本文研究了小波型dyadic结构函数系统的绝对收敛性，提出新的定量估计，证明了Weyl乘子的最优增长，并展示了去除正交性假设的通用结果。

Sufficient conditions for convergence of multiple Fourier series with $J_k$-lacunary sequence of rectangular partial sums in terms of Weyl multipliers

We obtain sufficient conditions for convergence (almost everywhere) of multiple trigonometric Fourier series of functions $f$ in $L_2$ in terms of Weyl multipliers. We consider the case where rectangular partial sums of Fourier series $S_n(x;f)$ have indices $n=(n_1,\dots,n_N) \in \mathbb Z^N$, $N\ge 3$, in which $k$ $(1\leq k\leq N-2)$ components on the places $\{j_1,\dots,j_k\}=J_k \subset \{1,\dots,N\} = M$ are elements of (single) lacunary sequences (i.e., we consider the, so called, multiple Fourier series with $J_k$-lacunary sequence of partial sums). We prove that for any sample $J_k\su…