A nicely behaved singular integral on a purely unrectifiable set
A nicely behaved singular integral on a purely unrectifiable set
We construct an example of a purely 1-unrectifiable AD-regular set $E$ in the plane such that the limit \[ \lim _{r\downarrow 0} \int \limits _{E\setminus B(x,r)} K(x-y) d \mathcal {H}^1 (y) \] exists and is finite for $\mathcal {H}^1$ almost every $x\in E$ for some class of antisymmetric Calderón-Zygmund kernels. …