The Cauchy problem for a class of hyperbolic operators with triple characteristics is analyzed. Some a priori estimates in Sobolev spaces with negative indexes are proved. Subsequently, an existence result for the Cauchy problem is obtained.

中文翻译：

---

一类具有三重特征的双曲算子的柯西问题

分析了一类具有三重特征的双曲算子的柯西问题。证明了Sobolev空间中具有负索引的一些先验估计。随后，获得了柯西问题的存在结果。