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Sharp Weighted $L^2$ inequalities for square functions

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arxiv 1603.07618 v1 pith:OZVHB66S submitted 2016-03-16 math.CA math.APmath.PR

Rodrigo Banuelos , Adam Osekowski This is my paper · ORCID
classification math.CAmath.APmath.PR
keywords functionssquareestimatesinequalitiesweightedanalyticapplicationapproach
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abstract

Using Bellman function approach, we present new proofs of weighted $L^2$ inequalities for square functions, with the optimal dependence on the $A_2$ characteristics of the weight and further explicit constants. We study the estimates both in the analytic and probabilistic context, and, as application, obtain related estimates for the classical Lusin and Littlewood-Paley square functions.

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  1. Weighted L\'epingle inequality

    math.PR 2019-08 conditional novelty 7.0 of 10

    For every p>1 and r>2, the weighted L_p norm of the pathwise r-variation of a martingale is bounded by C_p sqrt(r/(r-2)) times the A_p characteristic of the weight to a power, times the weighted L_p norm of the martingale.

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