1. Introduction A recent result by the author  establishes a pointwise control of an arbitrary measurable function in terms of its local mean oscillations. Soon after that, in a surprising work , D. Cruz-Uribe, J. Martell and C. P´erez showed that this result can be effectively applied in a variety of questions, including sharp weighted inequalities for classical singular integrals and the dyadic square function. In turn, based on  and on a recent concept of the intrinsic square function by M. Wilson , the author  obtained sharp weighted estimates for essentially any Littlewood-Paley operator. The aim of these notes is to present a unified, extended and almost self-contained exposition of the above-mentioned works [39, 12, 40].
|Original language||American English|
|Title of host publication||Function spaces, Approximation, Inequalities and Lineability, Lectures of the Spring School in Analysis, Matfyzpress, Prague (2011), .|
|Place of Publication||Prague|
|Number of pages||36|
|State||Published - 2011|
Bibliographical noteFunction spaces,
Approximation, Inequalities and Lineability, Lectures of the Spring School in Analysis,