Abstract
In this article, some necessary and sufficient conditions are shown in order that weighted inequality of the form
holds a.e. for uniformly integrable martingales f = (fn)n≥0 with some constant C > 0, where Φ1, Φ2 are Young functions, wi (i = 1, 2, 3, 4) are weights, \(f* = \mathop {\sup }\limits_{n \geqslant 0} \left| {f_n } \right|\) and \(f_\infty = \mathop {\lim }\limits_{n \to \infty } f_n\) a.e. As an application, two-weight weak type maximal inequalities of martingales are considered, and particularly a new equivalence condition is presented.
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Supported by the National Natural Science Foundation of China (11871195).
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Ren, Y. A Four-Weight Weak Type Maximal Inequality for Martingales. Acta Math Sci 39, 413–419 (2019). https://doi.org/10.1007/s10473-019-0207-5
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DOI: https://doi.org/10.1007/s10473-019-0207-5