We extend constructions of classical Clifford analysis to the case of indefinite non-degenerate quadratic forms. We define (p, q)-left- and right-monogenic functions by means of Dirac operators that factor a certain wave operator. We prove two different versions of Cauchy’s integral formulas for these functions. The two formulas arise from dealing with singularities in distinct ways, and are inspired by the methods of Frenkel and Libine (Adv Math 228:678–763, 2011) and Libine (Hypercomplex analysis and its applications, Birkhäuser, Boston, pp 161–180, 2011). These results indicate the merit of these methods for dealing with singularities.

我们将经典Clifford分析的构造扩展到不确定的非退化二次形式的情况。我们通过Dirac算子定义了（p，  q）-左单调函数和右单调函数，该函数会考虑某个波动算子。我们为这些函数证明了柯西积分公式的两个不同版本。这两个公式是通过以独特的方式处理奇点而产生的，并受到Frenkel和Libine（Adv Math 228：678-763，2011）和Libine（超复杂分析及其应用，Birkhäuser，波士顿，第161-180页）的启发。 ，2011）。这些结果表明了这些方法处理奇异点的优点。