Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gagliardo-Nirenberg, Trudinger-Moser and Morrey inequalities on
  Dirichlet spaces   With a view towards Riemannian or sub-Riemannian manifolds, RCD metric spaces
and specially fractals, this paper makes a step further in the development of a
theory of heat semigroup based $(1,p)$ Sobolev spaces in the general framework
of Dirichlet spaces. Under suitable assumptions that are verified in a variety
of settings, the tools developed by D. Bakry, T. Coulhon, M. Ledoux and L.
Saloff-Coste in the paper "Sobolev inequalities in disguise" allow us to obtain
the whole family of Gagliardo-Nirenberg and Trudinger-Moser inequalities with
optimal exponents. The latter depend not only on the Hausdorff and walk
dimensions of the space but also on other invariants. In addition, we prove
Morrey type inequalities and apply them to study the infimum of the exponents
that ensure continuity of Sobolev functions. The results are illustrated for
fractals using the Vicsek set, whereas several conjectures are made for nested
fractals and the Sierpinski carpet.

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The categories of this paper are: chem-ph
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The categories of this paper are: eess
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The categories of this paper are: alg-geom
16
The categories of this paper are: stat
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The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
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The categories of this paper are: atom-ph
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
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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: chao-dyn
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The categories of this paper are: ao-sci
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The categories of this paper are: q-fin
3
The categories of this paper are: physics
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The categories of this paper are: dg-ga