Eric T. Sawyer

Two-weight T1 theorem for fractional Riesz transforms: one measure supported on a $C^{1,\mathrm{Dini}}$ curve

Let $0\leq\alpha<n$, and let $\sigma$ and $\omega$ be locally finite positive Borel measures on $\R^n$, possibly with common point masses. Suppose that one measure is supported on a compact regular $C^{1,\mathrm{Dini}}$ curve. We prove that the $\alpha$-fractional Riesz vector maps $L^2(\sigma)$ to $L^2(\omega)$ if and...