Admissibility versus A<sub>p</sub>-Conditions on Regular Trees

Nguyen, Khanh Ngoc; Wang, Zhuang

doi:10.1515/agms-2020-0110

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2024

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Cited by 6 publications

(3 citation statements)

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“…A tree in [BBGS17,NgWa20] (or a weighted real line in [BBK06,BBS20]) is doubling, supports a Poincaré inequality and has more than one end.…”

Section: Introductionmentioning

confidence: 99%

Existence and uniqueness of limits at infinity for homogeneous Sobolev functions

Koskela¹,

Nguyen²

2022

Preprint

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We establish the existence and uniqueness of limits at infinity along infinite curves outside a zero modulus family for functions in a homogeneous Sobolev space under the assumption that the underlying space is equipped with a doubling measure which supports a Poincaré inequality. We also characterize the settings where this conclusion is nontrivial. Secondly, we introduce notions of weak polar coordinate systems and radial curves on metric measure spaces. Then sufficient and necessary conditions for existence of radial limits are given. As a consequence, we characterize the existence of radial limits in certain concrete settings.

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“…A tree in [BBGS17,NgWa20] (or a weighted real line in [BBK06,BBS20]) is doubling, supports a Poincaré inequality and has more than one end.…”

Section: Introductionmentioning

confidence: 99%

Existence and uniqueness of limits at infinity for homogeneous Sobolev functions

Koskela¹,

Nguyen²

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Recently, analysis on K-regular trees has been under development, see [3,21,22,23,20,27]. Let G be a K-regular tree with a set of vertices V and a set of edges E for some K ≥ 1.…”

Section: Introductionmentioning

confidence: 99%

“…whenever u is a measurable function on B(x, r) and g is an upper gradient of u, where u B(x,r) := − ´B(x,r) udµ = 1 µ(B(x,r)) ´B(x,r) udµ. The validity of a p-Poincaré inequality for X has very recently been characterized via a Muckenhoupt-type condition under a doubling condition on (X, d, µ), see [23] for more information.…”

Section: Introductionmentioning

confidence: 99%