We characterize the sets of solvability for Hermite multivariate interpolation problems when the sum of multiplicities is at most $2n + 2$, with $n$ the degree of the polynomial space. This result extends an earlier theorem (2000) by one of the authors concerning the case $2n+1$. The latter theorem, in turn, can be regarded as a natural extension of a classical Theorem of Severi (1921).

翻译：本文刻画了当重数之和不超过$2n+2$时Hermite多元插值问题的可解性集合，其中$n$为多项式空间的次数。该结果推广了作者之一在2000年针对$2n+1$情形所建立的定理。而该定理本身可视为Severi（1921）经典定理的自然延伸。