22 citations · 80 across the 66 of their papers we have counts for
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The Maz'ya-Shaposhnikova limit in the magnetic setting
Andrea Pinamonti, Marco Squassina, Eugenio Vecchi
We prove a magnetic version of the Maz'ya-Shaposhnikova singular limit of nonlocal norms with vanishing fractional parameter. This complements a general convergence result recently…
Magnetic BV functions and the Bourgain-Brezis-Mironescu formula
Andrea Pinamonti, Marco Squassina, Eugenio Vecchi
We prove a general magnetic Bourgain-Brezis-Mironescu formula. In particular, after developing a theory of magnetic bounded variation functions, we prove the validity of the formul…
Structure of Porous Sets in Carnot Groups
Andrea Pinamonti, Gareth Speight
We show that any Carnot group contains a closed nowhere dense set which has measure zero but is not -porous with respect to the Carnot-Carathéodory (CC) distance. In the first H…
Porosity, Differentiability and Pansu's Theorem
Andrea Pinamonti, Gareth Speight
We use porosity to study differentiability of Lipschitz maps on Carnot groups. Our first result states that directional derivatives of a Lipschitz function act linearly outside a $…