Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Characterization of Haj{\l}asz-Sobolev and Triebel-Lizorkin Spaces via
  Grand Littlewood-Paley Functions   In this paper, we establish the equivalence between the Haj{\l}asz-Sobolev
spaces or classical Triebel-Lizorkin spaces and a class of grand
Triebel-Lizorkin spaces on Euclidean spaces and also on metric spaces that are
both doubling and reverse doubling. In particular, when $p\in(n/(n+1),\infty)$,
we give a new characterization of the Haj{\l}asz-Sobolev spaces $\dot M^{1,
p}({\mathbb R}^n)$ via a grand Littlewood-Paley function.

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The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
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The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
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The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
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The categories of this paper are: q-fin
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The categories of this paper are: alg-geom
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The categories of this paper are: dg-ga
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The categories of this paper are: acc-phys
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The categories of this paper are: atom-ph