Two Weight Inequalities for the Cauchy Transform from $\mathbb{R}$ to ${\mathbb{C}}_{+}$

Michael T. Lacey, Eric T. Sawyer, Chun-Yen Shen +2

We characterize those pairs of weights $\sigma$ on $\mathbb{R}$ and $\tau$ on ${\mathbb{C}}_{+}$ for which the Cauchy transform $\mathsf{C}_σ f (z) \equiv \int_{\mathbb{R}} \frac {f(x)} {x…