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arXiv · 1705.04939

Weighted estimates for the multilinear maximal function on the upper half-spaces

Wei Chen·Chunxiang Zhu
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Abstract

For a general dyadic grid, we give a Calder\'{o}n-Zygmund type decomposition, which is the principle fact about the multilinear maximal function $\mathfrak{M}$ on the upper half-spaces. Using the decomposition, we study the boundedness of $\mathfrak{M}.$ We obtain a natural extension to the multilinear setting of Muckenhoupt's weak-type characterization. We also partially obtain characterizations of Muckenhoupt's strong-type inequalities with one weight. Assuming the reverse H\"{o}lder's condition, we get a multilinear analogue of Sawyer's two weight theorem. Moreover, we also get Hyt\"{o}nen-P\'{e}rez type weighted estimates.

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Wei Chen, Chunxiang Zhu. 2017-05-14. Weighted estimates for the multilinear maximal function on the upper half-spaces. https://arxiv.org/abs/1705.04939

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