Sobolev spaces and hyperbolic fillings
Let be an Ahlfors -regular compact metric measure space, where . For we introduce a new (fractional) Sobolev space consisting of functions whose extensions to the hyperbolic filling of satisfy a weak-type gradient condition. If supports a -Poincaré inequality with , then coincides with the familiar...
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| Published in | Journal für die reine und angewandte Mathematik Vol. 2018; no. 737; pp. 161 - 187 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
De Gruyter
01.04.2018
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| Online Access | Get full text |
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| Summary: | Let
be an Ahlfors
-regular compact metric measure space, where
. For
we introduce a new (fractional) Sobolev space
consisting of functions whose
extensions to the hyperbolic filling of
satisfy a weak-type
gradient condition. If
supports a
-Poincaré inequality with
, then
coincides with the familiar (homogeneous) Hajłasz–Sobolev space. |
|---|---|
| ISSN: | 0075-4102 1435-5345 |
| DOI: | 10.1515/crelle-2015-0036 |