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

Wei Chen and Chunxiang Zhu

Mathematische Nachrichten, 2019, vol. 292, issue 4, 777-792

Abstract: For a general dyadic grid, we give a Calderón–Zygmund type decomposition, which is the principle fact about the multilinear maximal function M on the upper half‐spaces. Using the decomposition, we study the boundedness of 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 Hölder's condition, we get a multilinear analogue of Sawyer's two weight theorem. Moreover, we also get Hytönen–Pérez type weighted estimates.

Date: 2019
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https://doi.org/10.1002/mana.201700376

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