Haar basis testing

Michel Alexis, Jose Luis Luna-Garcia, Eric T. Sawyer

We show that for two doubling measures $\ddot{I}ƒ$ and $\ddot{I}‰$ on ${\mathbb{R}}^n$ and any fixed dyadic grid $\mathcal{D}$ in ${\mathbb{R}}^n$, \[ \mathfrak{N}_{\mathbf{R}^{λ, n}}\left( σ,…