We study the properties of the dual Sobolev space H-1;q(X) = - H1;p(X) '0 on a complete extended metric-topological measure space X = (X; ⊤; d;m) for p 2 (1;1). We will show that a crucial role is played by the strong closure H-1;q pd (X) of Lq(X;m) in the dual H-1;q(X), which can be identified with the predual of H1;p(X). We will show that positive functionals in H-1;q(X) can be represented as a positive Radon measure and we will charaterize their dual norm in terms of a suitable energy functional on nonparametric dynamic plans. As a byproduct, we will show that for every Radon measure μ with finite dual Sobolev energy, Capp-negligible sets are also μ-negligible and good representatives of Sobolev functions belong to L1(X; μ). We eventuall...
AbstractWe prove tightness of (r,p)-Sobolev capacities on configuration spaces equipped with Poisson...
AbstractA dual capacitary Brunn–Minkowski inequality is established for the (n−1)-capacity of radial...
In this paper we make a survey of some recent developments of the theory of Sobolev spaces W1,q(X, ...
We study the properties of the dual Sobolev space H--1,H-q (X) = (H-1,H-p(X))' on a complete extende...
We discuss the potential theory related to variational capacity and the Sobolev capacity on metric m...
We study the properties of the Sobolev Multiplier Spaces of X-valued functions and their preduals, w...
We show that capacity can be computed with locally Lipschitz functions in locally complete and separ...
We study the properties of the Sobolev Multiplier Spaces of X-valued functions and their preduals, w...
We prove a general criterion for the density in energy of suitable subalgebras of Lipschitz function...
In a complete metric space equipped with a doubling measure and supporting a $(1,1)$-Poincar\'e ineq...
We provide new characterizations of Sobolev ad BV spaces in doubling and Poincaré metric spaces in t...
Abstract. This paper studies the relative Sobolev p-capacity in proper and un-bounded doubling metri...
Generalizing work of Li and Wang, we prove sharp volume growth/decay rates for ends of metric measur...
We prove a general criterion for the density in energy of suitable subalgebras of Lipschitz function...
Given a subset $E$ of $\R^n$ with empty interior and an integrability parameter $1<p<\infty$, what i...
AbstractWe prove tightness of (r,p)-Sobolev capacities on configuration spaces equipped with Poisson...
AbstractA dual capacitary Brunn–Minkowski inequality is established for the (n−1)-capacity of radial...
In this paper we make a survey of some recent developments of the theory of Sobolev spaces W1,q(X, ...
We study the properties of the dual Sobolev space H--1,H-q (X) = (H-1,H-p(X))' on a complete extende...
We discuss the potential theory related to variational capacity and the Sobolev capacity on metric m...
We study the properties of the Sobolev Multiplier Spaces of X-valued functions and their preduals, w...
We show that capacity can be computed with locally Lipschitz functions in locally complete and separ...
We study the properties of the Sobolev Multiplier Spaces of X-valued functions and their preduals, w...
We prove a general criterion for the density in energy of suitable subalgebras of Lipschitz function...
In a complete metric space equipped with a doubling measure and supporting a $(1,1)$-Poincar\'e ineq...
We provide new characterizations of Sobolev ad BV spaces in doubling and Poincaré metric spaces in t...
Abstract. This paper studies the relative Sobolev p-capacity in proper and un-bounded doubling metri...
Generalizing work of Li and Wang, we prove sharp volume growth/decay rates for ends of metric measur...
We prove a general criterion for the density in energy of suitable subalgebras of Lipschitz function...
Given a subset $E$ of $\R^n$ with empty interior and an integrability parameter $1<p<\infty$, what i...
AbstractWe prove tightness of (r,p)-Sobolev capacities on configuration spaces equipped with Poisson...
AbstractA dual capacitary Brunn–Minkowski inequality is established for the (n−1)-capacity of radial...
In this paper we make a survey of some recent developments of the theory of Sobolev spaces W1,q(X, ...