Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $\mathrm{L}^1$-estimates for constant rank operators   We show that the inequality $$
  \|D^{k-1}(u-\pi u)\|_{\mathrm{L}^{n/(n-1)}(\mathbb{R}^n)}\leq
c\|\mathbb{B}(D) u\|_{\mathrm{L}^1(\mathbb{R}^n)} $$ holds for vector fields
$u\in\mathrm{C}^\infty_c$ if and only if $\mathbb{B}$ is canceling. Here $\pi$
denotes the $\mathrm{L}^2$-orthogonal projection onto the kernel of the
$k$-homogeneous differential operator $\mathbb{B}(D)$ of \emph{constant rank}
on $\mathbb{R}^n$. Other critical embeddings are established.

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The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
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The categories of this paper are: hep-lat
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The categories of this paper are: ao-sci
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The categories of this paper are: nlin
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The categories of this paper are: stat
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The categories of this paper are: adap-org
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The categories of this paper are: hep-th
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The categories of this paper are: patt-sol
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The categories of this paper are: math-ph
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The categories of this paper are: econ
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The categories of this paper are: gr-qc
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The categories of this paper are: solv-int
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-th
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The categories of this paper are: quant-ph