The paper contains a study of weighted exponential inequalities for differentially subordinate martingales, under the assumption that the underlying weight satisfies Muckenhoupt’s condition \(A_{\infty }\). The proof exploits certain functions enjoying appropriate size conditions and concavity. The martingales are adapted, uniformly integrable, and càdlàg - we do not assume any path-continuity restrictions. Because of this generality, we need to handle jump parts of processes which forces us to construct a Bellman function satisfying a stronger condition than local concavity. As a corollary, we will establish some new weighted \(L^p\) estimates for differential subordinates of bounded martingales.

假设基础权重满足Muckenhoupt条件\（A _ {\ infty} \），则本文对差分从属mar的加权指数不等式进行了研究。证明利用享有适当大小条件和凹度的某些功能。适应性强，统一可整合性和可移动性-我们不假设任何路径连续性限制。由于这种通用性，我们需要处理过程的跳跃部分，这迫使我们构造满足比局部凹面更强条件的Bellman函数。作为推论，我们将为有限mar的差分下属建立一些新的加权\（L ^ p \）估计。