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arXiv · 1512.00663

The existence and boundedness of multilinear Marcinkiewicz integrals on Companato spaces

Qingying Xue·Kozo Yabuta
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Abstract

In this paper, we established the boundedness of m-linear Marcinkiewicz integral on Campanato type spaces. We showed that if the $m$-linear Marcinkiewicz integral is finite for one point, then it is finite almost everywhere. Moreover, the following norm inequality holds, $$\|μ(\vec{f})\|_{\mathcal{E}^{α,p}} \leq C\prod_{j=1}^m\|f_j\|_{\mathcal{E}^{α_j,p_j}},$$ where $\mathcal{E}^{α,p}$ is the classical Campanato spaces.

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Qingying Xue, Kozo Yabuta. 2015-12-02. The existence and boundedness of multilinear Marcinkiewicz integrals on Companato spaces. https://arxiv.org/abs/1512.00663

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