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arXiv · 1811.05209

Sharp reverse H\"older inequality for $C_p$ weights and applications

Javier Canto
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Abstract

We prove an appropriate sharp quantitative reverse H\"older inequality for the $C_p$ class of weights from which we obtain as a limiting case the sharp reverse H\"older inequality for the $A_\infty$ class of weights. We use this result to provide a quantitative weighted norm inequality between Calder\'on-Zygmund operators and the Hardy-Littlewood maximal function, precisely \[ \|Tf\|_{L^p(w)} \lesssim_{T,n,p,q} [w]_{C_q}(1+\log^+[w]_{C_q})\|Mf\|_{L^p(w)}, \] for $w\in C_q$ and $q>p>1$, quantifying Sawyer's theorem.

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Javier Canto. 2018-11-13. Sharp reverse H\"older inequality for $C_p$ weights and applications. https://doi.org/10.1007/s12220-020-00430-1

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