$L^2$-bounded singular integrals on a purely unrectifiable set in ${\mathbb{R}}^d$

Joan Mateu, Laura Prat

We construct an example of a purely unrectifiable measure $\mu$ in ${\mathbb{R}}^d$ for which the singular integrals associated to the kernels $\displaystyle{K(x)=\frac{P_{2k+1}(x)}{|x…