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arXiv · 1602.06583

A quantitative approach to weighted Carleson Condition

Israel P. Rivera-Ríos
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Abstract

Quantitative versions of weighted estimates obtained by F. Ruiz and J.L. Torrea in the 80's for the operator \[ \mathcal{M}f(x,t)=\sup_{x\in Q,\,l(Q)\geq t}\frac{1}{|Q|}\int_{Q}|f(x)|dx \qquad x\in\mathbb{R}^{n}, \, t \geq0 \] are obtained. As a consequence, some sufficient conditions for the boundedness of $\mathcal{M}$ in the two weight setting in the spirit of the results obtained by C. P\'erez and E. Rela and very recently by M.T. Lacey and S. Spencer for the Hardy-Littlewood maximal operator are derived. As a byproduct some new quantitative estimates for the Poisson integral are obtained.

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Israel P. Rivera-Ríos. 2016-02-21. A quantitative approach to weighted Carleson Condition. https://doi.org/10.1515/conop-2017-0006

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