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2016 Weighted maximal inequality for differentially subordinate martingales
Adam Osȩkowski
Electron. Commun. Probab. 21: 1-10 (2016). DOI: 10.1214/16-ECP4586


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.


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Adam Osȩkowski. "Weighted maximal inequality for differentially subordinate martingales." Electron. Commun. Probab. 21 1 - 10, 2016.


Received: 25 September 2015; Accepted: 28 February 2016; Published: 2016
First available in Project Euclid: 10 March 2016

zbMATH: 1338.60122
MathSciNet: MR3485392
Digital Object Identifier: 10.1214/16-ECP4586

Primary: 60G44

Keywords: Differential subordination , martingale , maximal inequality , weight

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