Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Homogeneous algebras via heat kernel estimates   We study homogeneous Besov and Triebel--Lizorkin spaces defined on doubling
metric measure spaces in terms of a self-adjoint operator whose heat kernel
satisfies Gaussian estimates together with its derivatives. When the measure
space is a smooth manifold and such operator is a sum of squares of smooth
vector fields, we prove that their intersection with $L^\infty$ is an algebra
for pointwise multiplication. Our results apply to nilpotent Lie groups and
Grushin settings.

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The categories of this paper are: math-ph
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The categories of this paper are: nlin
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The categories of this paper are: q-alg
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The categories of this paper are: atom-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-th
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The categories of this paper are: q-bio
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The categories of this paper are: cmp-lg
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ex
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The categories of this paper are: stat
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The categories of this paper are: cond-mat
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The categories of this paper are: mtrl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: adap-org