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We are interested in the study of the space of $n$-ary differential operatorsdenoted by $\mathfrak{D}_{\underline{\l},\mu}$ where$\underline{\l}=(\l_{1},...,\l_{n})$ acting on weighted densities from $\frakF_{\l_1}\otimes\frak F_{\l_2}\otimes...\otimes\frak F_{\l_n}$ to $\frakF_{\mu}$ as a module over the orthosymplectic superalgebra$\mathfrak{osp}(1|2)$. As a consequence, we prove the existence and theuniqueness of a canonical conformally equivariant symbol map from$\mathfrak{D}_{\underline{\lambda},\mu}^k$ to the corresponding space ofsymbols as well for the explicit expression of the associated quantization map.

Conformally equivariant quantization and symbol maps associated with $n$-ary differential operators on weighted densities