Weighted square function estimates

The paper contains the proof of \(L^p\)-weighted norm inequalities for both, martingales square functions and the classical square functions in harmonic analysis of Littlewood-Paley and Lusin. Furthermore, the bounds are completely explicit and are optimal not only on the dependence of the character...

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Bibliographic Details
Published in:arXiv.org 2017-11
Main Authors: Banuelos, Rodrigo, Osekowski, Adam
Format: Article
Language:English
Subjects:
Dependence
Fourier analysis
Harmonic analysis
Harmonic functions
Martingales
Mathematical analysis
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Online Access:Get full text
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Summary:The paper contains the proof of \(L^p\)-weighted norm inequalities for both, martingales square functions and the classical square functions in harmonic analysis of Littlewood-Paley and Lusin. Furthermore, the bounds are completely explicit and are optimal not only on the dependence of the characteristics of the weight but also on the dependance on \(p\), as \(p\to\infty\). The proof rests on Bellman function method: the estimates are deduced from the existence of an appropriate and rather complicated function of four variables.
ISSN:2331-8422