4 problems

Let $d\geq 2$, let $s>0$, and set $1/\tau=s/(d-1)$. The relevant approximation error is measured in the Triebel–Lizorkin space $\mathcal{F}^{0q}_\infty(\mathbb{S}^{d-1})$ using non…

Let $T$ be the central cell of a uniform grid, let $S$ be the stencil consisting of the nine cells used by the measurement map, and define $V_{2,T}$ as the indicators of half-plane…

Let $d\geqslant2$, and consider the higher-dimensional analogue of the class ${\cal F}_{s,R,M}$ of indicator functions with regular boundaries. Uniform piecewise constant approxima…

Let ${\cal F}_{s,R,M}$ be the class of characteristic functions of domains in $[0,1]^2$ whose boundaries have the regularity specified in the paper, and let linear reconstruction m…