2 problems

Weighted maximal operator conjecture. For every $f\in H_1$, the operator $S^{\ast,\nabla}$ is bounded from $H_1$ to $L_1$. Moreover, if $\sup_{k\in\mathbb{N}}|A_{n_k}|=\infty$ and…

Let $\{n_j:j\ge 1\}$ be a lacunary sequence of integers, meaning that … For a function $f$ on $\mathbb T$, let $S_{n_j}f$ denote its Walsh-Fourier partial sums, and write…