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math.FA2013★ 2 cited
Hajlasz Gradients Are Upper Gradients
Renjin Jiang, Nageswari Shanmugalingam, Dachun Yang +1
Let be a metric measure space, with a Borel regular measure. In this paper, we prove that, if and is a Hajłasz gradient…
math.FA2013★ 29 cited
Geometric analysis on Cantor sets and trees
Anders Björn, Jana Björn, James T. Gill +1
Using uniformization, Cantor type sets can be regarded as boundaries of rooted trees. In this setting, we show that the trace of a first-order Sobolev space on the boundary of a re…