32 citations · 140 across the 39 of their papers we have counts for
20 papers · 1 filter
A Bochner-type integration theory for random normed modules
Andrea Kubin, Enrico Pasqualetto
We develop a measure and integration theory for random normed modules. Given a probability space , we introduce and study measures taking values into the s…
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…
An axiomatic theory of normed modules via Riesz spaces
Danka Lučić, Enrico Pasqualetto
We introduce and study an axiomatic theory of -normed -modules, where is a Riesz space and is an -algebra; the spaces and also have some additional structu…
Vector calculus on weighted reflexive Banach spaces
Enrico Pasqualetto, Tapio Rajala
We study first-order Sobolev spaces on reflexive Banach spaces via relaxation, test plans, and divergence. We show the equivalence of the different approaches to the Sobolev spaces…
Maps of bounded variation from PI spaces to metric spaces
Camillo Brena, Francesco Nobili, Enrico Pasqualetto
We study maps of bounded variation defined on a metric measure space and valued into a metric space. Assuming the source space to satisfy a doubling and Poincaré property, we produ…
Sobolev and BV functions on spaces via the short-time behaviour of the heat kernel
Camillo Brena, Enrico Pasqualetto, Andrea Pinamonti
In the setting of finite-dimensional spaces, we characterize the -Sobolev spaces for and the space of functions of bounded variation in term…
Limits and colimits in the category of Banach -modules
Enrico Pasqualetto
We prove that the category of Banach -modules over a given -finite measure space is both complete and cocomplete, which means that it admits all small limits and colimits.
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…
On the reflexivity properties of Banach bundles and Banach modules
Milica Lučić, Enrico Pasqualetto, Ivana Vojnović
In this paper we investigate some reflexivity-type properties of separable measurable Banach bundles over a -finite measure space. Our two main results are the following: - The…
A short proof of the existence of master test plans
Enrico Pasqualetto
The aim of this brief note is to provide a quick and elementary proof of the following known fact: on a metric measure space whose Sobolev space is separable, there exists a test p…
The metric-valued Lebesgue differentiation theorem in measure spaces and its applications
Danka Lučić, Enrico Pasqualetto
We prove a version of the Lebesgue Differentiation Theorem for mappings that are defined on a measure space and take values into a metric space, with respect to the differentiation…
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…
Characterisation of upper gradients on the weighted Euclidean space and applications
Danka Lučić, Enrico Pasqualetto, Tapio Rajala
In the context of Euclidean spaces equipped with an arbitrary Radon measure, we prove the equivalence among several different notions of Sobolev space present in the literature and…
Testing the Sobolev property with a single test plan
Enrico Pasqualetto
We prove that in a vast class of metric measure spaces (namely, those whose associated Sobolev space is separable) the following property holds: a single test plan can be used to r…
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…
Quasi-continuous vector fields on RCD spaces
Clément Debin, Nicola Gigli, Enrico Pasqualetto
In the existing language for tensor calculus on RCD spaces, tensor fields are only defined m-a.e.. In this paper we introduce the concept of tensor field defined `2-capacity-a.e.'…
Direct and inverse limits of normed modules
Enrico Pasqualetto
The aim of this note is to study existence and main properties of direct and inverse limits in the category of normed -modules (in the sense of Gigli) over a metric measure sp…
Differential of metric valued Sobolev maps
Nicola Gigli, Enrico Pasqualetto, Elefterios Soultanis
We introduce a notion of differential of a Sobolev map between metric spaces. The differential is given in the framework of tangent and cotangent modules of metric measure spaces,…
Differential structure associated to axiomatic Sobolev spaces
Nicola Gigli, Enrico Pasqualetto
The aim of this note is to explain in which sense an axiomatic Sobolev space over a general metric measure space (à la Gol'dshtein-Troyanov) induces - under suitable locality assum…