22 citations · 43 across the 4 of their papers we have counts for
4 papers
A simple proof of reflexivity and separability of Sobolev spaces
Ryan Alvarado, Piotr Hajłasz, Lukáš Malý
We present an elementary proof of a well-known theorem of Cheeger which states that if a metric-measure space supports a -Poincaré inequality, then the Sobolev…
Trace and extension theorems for Sobolev-type functions in metric spaces
Lukáš Malý
Trace classes of Sobolev-type functions in metric spaces are subject of this paper. In particular, functions on domains whose boundary has an upper codimension- bound are consid…
Minimal weak upper gradients in Newtonian spaces based on quasi-Banach function lattices
Lukáš Malý
Properties of first-order Sobolev-type spaces on abstract metric measure spaces, so-called Newtonian spaces, based on quasi-Banach function lattices are investigated. The set of al…
Newtonian spaces based on quasi-Banach function lattices
Lukáš Malý
In this paper, first-order Sobolev-type spaces on abstract metric measure spaces are defined using the notion of (weak) upper gradients, where the summability of a function and its…