Lusin-type Theorems for Cheeger Derivatives on Metric Measure Spaces

• Autorzy: Guy C. David
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Lipschitz; Lusin; PI space; Poincaré inequality; measurable differentiable structure

• Wydawca: De Gruyter Open
• Czasopismo: Analysis and Geometry in Metric Spaces
• Rocznik: 2015
• Tom: 3
• Numer: 1

Daty

otrzymano

2015-02-05

zaakceptowano

2015-09-15

online

2015-10-15

Twórcy

autor

Guy C. David

• Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012

Bibliografia

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Identyfikatory

DOI

10.1515/agms-2015-0017