2 problems

Let $\mathcal{D}$ be the dyadic rectangles in $[0,1)^d$, and for each $R\in\mathcal{D}$ let $h_R$ denote its associated Haar function. For signs $\varepsilon_R\in\{-1,1\}$, conside…

For an even integer $n$, let $H_I(\mathbf x)$ be the $d$-dimensional Haar function indexed by a dyadic rectangle $I$, let $|I|$ denote the measure of $I$, and let $c_I$ be arbitrar…