Restricted Beurling transforms on Campanato spaces
  Let $\Omega\subset \mathbb{C}$ be a bounded domain with $\mathcal{C}^{1,\omega}$-smooth boundary, where $\omega$ is a Dini-smooth modulus of continuity. We prove that the restricted Beurling transform is bounded on the Campanato space $\mathrm{BMO}_\omega(\Omega)$. 
Evgueni Doubtsov and Andrei V. Vasin
math.CV