7 problems

Let $F_k$ and $G_k$ be the arithmetic Fourier series considered in the paper, and let $q_n(x)$ denote the denominators of the continued-fraction convergents of $x$. Let…

Let $\mathbb{T}$ be the unit circle, let $dm$ denote normalized Lebesgue measure on $\mathbb{T}$, and let $L^2(\mathbb{T})$ be the space of square-integrable functions on…

Strong summability conjecture. There exists an absolute constant $c$ such that

Let $H_p^{\square}(G_m^2)$ denote the two-dimensional martingale Hardy space and let $M_k$ be the associated scale sequence. For $f$ in these spaces, write…

Convergence-rate conjecture. There exists an absolute constant $c$ such that

Weierstrass-type conjecture. The Fourier series above represents a function of the Weierstrass type that is continuous but nowhere differentiable.

Fourier series are understood in their usual partial-sum sense, and $L\log L$ denotes the Orlicz class associated with the growth function $t\mapsto t\log({\rm e}+t)$. The…