Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Extension and trace theorems for noncompact doubling spaces   We generalize the extension and trace results of
Bj\"orn-Bj\"orn-Shanmugalingam \cite{BBS21} to the setting of complete
noncompact doubling metric measure spaces and their uniformized hyperbolic
fillings. This is done through a uniformization procedure introduced by the
author that uniformizes a Gromov hyperbolic space using a Busemann function
instead of the distance functions considered in the work of
Bonk-Heinonen-Koskela \cite{BHK}. We deduce several corollaries for the Besov
spaces that arise as trace spaces in this fashion, including the existence of
representatives that are quasicontinuous with respect to the Besov capacity,
the existence of $L^p$-Lebesgue points quasieverywhere with respect to the
Besov capacity, embeddings into H\"older spaces for appropriate exponents, and
a stronger Lebesgue point result under an additional reverse doubling
hypothesis on the measure. We also obtain several Poincar\'e-type inequalities
relating integrals of Besov functions over balls to integrals of upper
gradients of extension of these functions to a uniformized hyperbolic filling
of the space.

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The categories of this paper are: mtrl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: acc-phys
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The categories of this paper are: chao-dyn
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The categories of this paper are: supr-con
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The categories of this paper are: patt-sol
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The categories of this paper are: chem-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
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The categories of this paper are: cond-mat
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The categories of this paper are: physics
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The categories of this paper are: nlin
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-th