Weighted square function estimates

Rodrigo Banuelos; Adam Osekowski

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arXiv · 1711.08754

Weighted square function estimates

Rodrigo Banuelos·Adam Osekowski

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Abstract

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.

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BibTeX RIS

Rodrigo Banuelos, Adam Osekowski. 2017-11-23. Weighted square function estimates. https://arxiv.org/abs/1711.08754

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