3 problems

For positive integers $n,m$, a function $\psi: \mathbb{N} \to \mathbb{R}_{\geq 0}$, and an inhomogeneous parameter $\mathbf{y} \in \mathbb{R}^m$, let…

Let $n,m$ be positive integers with $nm=2$, and let $\Psi=(B_q)_{q\in\mathbb{N}}$ be any sequence of balls in $\mathbb{R}^m/\mathbb{Z}^m$. Let $\mathcal A_{n,m}(\Psi)$ denote the c…

Let $n,m$ be positive integers with $nm=2$, let $\psi:\mathbb{N}\to\mathbb{R}_{\geq 0}$, and let $\mathbf{y}\in\mathbb{R}^m$. Let $\mathcal A_{n,m}^{\mathbf{y}}(\psi)$ denote the s…