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Over the $(1,n)$-dimensional real supercircle, we consider the$\mathcal{K}(n)$-modules of linear differential operators,$\frak{D}^n_{\lambda,\mu}$, acting on the superspaces of weighted densities,where $\mathcal{K}(n)$ is the Lie superalgebra of contact vector fields. Wegive, in contrast to the classical setting, a classification of these modulesfor $n=1$. We also prove that $\frak{D}^{n}_{\lambda,\mu}$ and$\frak{D}_{\rho,\nu}^{n}$ are isomorphic for $\rho=\frac{2-n}{2}-\mu$ and$\nu=\frac{2-n}{2}-\lambda$. This work is the simplest superization of a resultby Gargoubi and Ovsienko [Modules of Differential Operators on the Real Line,Functional Analysis and Its Applications, Vol. 35, No. 1, pp. 13--18, 2001.]

Differential Operators on the Weighted Densities on the Supercircle $S^{1|n}$