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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
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