Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The existence and boundedness of multilinear Marcinkiewicz integrals on
  Companato spaces   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,
$$\|\mu(\vec{f})\|_{\mathcal{E}^{\alpha,p}} \leq
C\prod_{j=1}^m\|f_j\|_{\mathcal{E}^{\alpha_j,p_j}},$$ where
$\mathcal{E}^{\alpha,p}$ is the classical Campanato spaces.

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The categories of this paper are: nlin
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The categories of this paper are: supr-con
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The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
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The categories of this paper are: mtrl-th
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The categories of this paper are: math-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: solv-int
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The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: econ
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The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
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The categories of this paper are: dg-ga