27 citations · 32 across the 8 of their papers we have counts for
8 papers
Metric Sobolev spaces I: equivalence of definitions
Luigi Ambrosio, Toni Ikonen, Danka Lučić +1
This is the first of two works concerning the Sobolev calculus on metric measure spaces and its applications. In this work, we focus on several notions of metric Sobolev space and…
On the integration of Banach modules and its applications to vector calculus on spaces
Emanuele Caputo, Milica Lučić, Enrico Pasqualetto +1
A finite-dimensional space can be foliated into sufficiently regular leaves, where a differential calculus can be performed. Two important examples are given by the mea…
Projective and injective tensor products of Banach -modules
Enrico Pasqualetto
We study projective and injective tensor products of Banach -modules over a -finite measure space. En route, we extend to Banach -modules several technical tools of in…
Variational problems concerning length distances in metric spaces
Fares Essebei, Enrico Pasqualetto
Given a locally compact, complete metric space and an open set , we study the class of length distances on that are bounded from…
Duals and pullbacks of normed modules
Nicola Gigli, Danka Lučić, Enrico Pasqualetto
We give a general description of the dual of the pullback of a normed module. Ours is the natural generalization to the context of modules of the well-known fact that the dual of t…
Pullback of a quasiconformal map between arbitrary metric measure spaces
Toni Ikonen, Danka Lučić, Enrico Pasqualetto
We prove that every (geometrically) quasiconformal homeomorphism between metric measure spaces induces an isomorphism between the cotangent modules constructed by Gigli. We obtain…