Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Anisotropic $L^{2}$-weighted Hardy and $L^{2}$-Caffarelli-Kohn-Nirenberg
  inequalities   We establish sharp remainder terms of the $L^{2}$-Caffarelli-Kohn-Niren\-berg
inequalities on homogeneous groups, yielding the inequalities with best
constants. Our methods also give new sharp Caffarelli-Kohn-Nirenberg type
inequalities in $\mathbb{R}^{n}$ with arbitrary quasi-norms. We also present
explicit examples to illustrate our results for different weights and in
abelian cases.

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The categories of this paper are: hep-ph
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The categories of this paper are: funct-an
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The categories of this paper are: gr-qc
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The categories of this paper are: alg-geom
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-lat
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The categories of this paper are: math-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: mtrl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: econ
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-ex
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The categories of this paper are: cond-mat