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A note on BV and 1-Sobolev functions on the weighted Euclidean space
Maria Stella Gelli, Danka Lučić
In the setting of the Euclidean space equipped with an arbitrary Radon measure, we prove the equivalence between several notions of function of bounded variation present in the lit…
Representation theorems for normed modules
Simone Di Marino, Danka Lučić, Enrico Pasqualetto
In this paper we study the structure theory of normed modules, which have been introduced by Gigli. The aim is twofold: to extend von Neumann's theory of liftings to the framework…
A short proof of the infinitesimal Hilbertianity of the weighted Euclidean space
Simone Di Marino, Danka Lučić, Enrico Pasqualetto
We provide a quick proof of the following known result: the Sobolev space associated with the Euclidean space, endowed with the Euclidean distance and an arbitrary Radon measure, i…