Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: PI space

Sortuj według:

Ogranicz wyniki do:

Inverse Limit Spaces Satisfying a Poincaré Inequality

100%

Cheeger J., Kleiner B.

Analysis and Geometry in Metric Spaces

2015

tom 3

nr 1

We give conditions on Gromov-Hausdorff convergent inverse systems of metric measure graphs which imply that the measured Gromov-Hausdorff limit (equivalently, the inverse limit) is a PI space i.e., it satisfies a doubling condition and a Poincaré inequality in the sense of Heinonen-Koskela [12]. The Poincaré inequality is actually of type (1, 1). We also give a systematic construction of examples for which our conditions are satisfied. Included are known examples of PI spaces, such as Laakso spaces, and a large class of new examples. As follows easily from [4], generically our examples have the property that they do not bilipschitz embed in any Banach space with Radon-Nikodym property. For Laakso spaces, thiswas noted in [4]. However according to [7] these spaces admit a bilipschitz embedding in L1. For Laakso spaces, this was announced in [5].

Lusin-type Theorems for Cheeger Derivatives on Metric Measure Spaces

88%

David G. C. D.

Analysis and Geometry in Metric Spaces

2015

tom 3

nr 1

A theorem of Lusin states that every Borel function onRis equal almost everywhere to the derivative of a continuous function. This result was later generalized to Rn in works of Alberti and Moonens-Pfeffer. In this note, we prove direct analogs of these results on a large class of metric measure spaces, those with doubling measures and Poincaré inequalities, which admit a form of differentiation by a famous theorem of Cheeger.

Ograniczanie wyników

2 Analysis and Geometry in Metric Spaces

1 Cheeger J.

1 David G. C. D.

1 Kleiner B.

2 2015

Wyniki wyszukiwania

Inverse Limit Spaces Satisfying a Poincaré Inequality

Lusin-type Theorems for Cheeger Derivatives on Metric Measure Spaces