Weighted maximal inequality for differentially subordinate martingales.(English)Zbl 1338.60122

Summary: We establish a weighted maximal $$L^1$$-inequality for differentially subordinate martingales taking values in $$\mathbb{R} ^\nu$$, $$\nu \geq 1$$, under the assumption that the weight satisfies Muckenhoupt’s condition $$A_1$$. An optimal dependence of the constant on the $$A_1$$ characteristics is identified.

MSC:

 60G44 Martingales with continuous parameter
Full Text: