T. Le

Square Functions and Rectifiability under Monotone Transformations of the Density

Let $\mu$ be an $n$-AD-regular measure in $\mathbb{R}^d$. Chousionis, Garnett, Le and Tolsa [CGLT] proved that $\mu$ is uniformly $n$-rectifiable if and only if the square function built from the density differences $\Delta_\mu(x,r)=\mu(B(x,r))/r^n-\mu(B(x,2r))/(2r)^n$ satisfies a Carleson condition. In this paper we s...