The Boutet de Monvel operators in variable Hölder–Zygmund spaces on $\mathbb{R}^{n}_+$

We consider Green operators from the Boutet de Monvel algebra in the Hölder–Zygmund spaces of variable smoothness on $\overline{\mathbb R}^{n}_+$. The order of smoothness depends on a point in the domain and may take negative values. The sufficient conditions of boundedness of the Boutet de Monvel operators are obtained.