Weighted 𝐿² inequalities for square functions

Bañuelos, Rodrigo; Osȩkowski, Adam

doi:10.1090/tran/7056

Weighted $L^2$ inequalities for square functions
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by Rodrigo Bañuelos and Adam Osȩkowski PDF

Trans. Amer. Math. Soc. 370 (2018), 2391-2422 Request permission

Abstract:

Using the 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 an application, obtain related estimates for the classical Lusin and Littlewood-Paley square functions.

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