Let \((X, d, \mu )\) be a space of homogeneous type with a metric d and a doubling measure \(\mu \). Assume that \(\rho \) is a critical function on X which has an associated class of weights containing the Muckenhoupt weights as a proper subset. In this paper, we prove the quantitative weighted estimates for certain singular integrals corresponding to the new class of weights. It is important to note that the assumptions on the kernels of these singular integrals do not have any regularity conditions. Our applications include the spectral multipliers and the Riesz transforms associated to Schrödinger operators in various settings, ranging from the magnetic Schrödinger operators in Euclidean spaces to the Laguerre operators.

令\（（X，d，\ mu）\）是具有度量d和加倍度量\（\ mu \）的齐次类型空间。假设\（\ rho \）是X上的关键函数它具有相关的权重类别，其中包含Muckenhoupt权重作为适当的子集。在本文中，我们证明了对应于新一类权重的某些奇异积分的定量加权估计。重要的是要注意，这些奇异积分的核的假设没有任何正则条件。我们的应用包括频谱乘法器和与Schrödinger算符相关联的Riesz变换的各种设置，从欧几里得空间中的磁性Schrödinger算符到Laguerre算符。