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<p>In this paper, we consider the weighted weak type (1,&#xa0;1) inequality of the operator associated with the differences of noncommutative dyadic differential operators and martingales. This extends the main result of [<CitationRef CitationID="CR31">31</CitationRef>] to the weighted setting. Additionally, we prove the weighted weak type (1,&#xa0;1) inequality for noncommutative martingale transforms. These two inequalities enable us to derive the result of differential transforms converging in measure, which establishes the noncommutative analogue of the result of [<CitationRef CitationID="CR17">17</CitationRef>] in the weighted setting.</p>

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Weighted estimates for noncommutative differential operators and martingales

  • 期刊论文

  • 发表日期：

    2026年1月10日

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  • Junming Cao,
  • Xingyan Quan

摘要

In this paper, we consider the weighted weak type (1, 1) inequality of the operator associated with the differences of noncommutative dyadic differential operators and martingales. This extends the main result of [31] to the weighted setting. Additionally, we prove the weighted weak type (1, 1) inequality for noncommutative martingale transforms. These two inequalities enable us to derive the result of differential transforms converging in measure, which establishes the noncommutative analogue of the result of [17] in the weighted setting.