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arXiv · 1504.03420

On multilinear fractional strong maximal operator associated with rectangles and multiple weights

Mingming Cao·Qingying Xue·Kozo Yabuta
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Abstract

In this paper, the multilinear fractional strong maximal operator $\mathcal{M}_{\mathcal{R},\alpha}$ associated with rectangles and corresponding multiple weights $A_{(\vec{p},q),\mathcal{R}}$ are introduced. Under the dyadic reverse doubling condition, a necessary and sufficient condition for two-weight inequalities is given. As consequences, we first obtain a necessary and sufficient condition for one-weight inequalities. Then, we give a new proof for the weighted estimates of multilinear fractional maximal operator $\mathcal{M}_\alpha$ associated with cubes and multilinear fractional integral operator $\mathcal{I}_{\alpha}$, which is quite different and simple from the proof known before.

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Mingming Cao, Qingying Xue, Kozo Yabuta. 2015-04-14. On multilinear fractional strong maximal operator associated with rectangles and multiple weights. https://arxiv.org/abs/1504.03420

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