相关论文: New Characterizations of First Order Sobolev Space…

We prove uniform boundedness of certain boundary representations on appropriate fractional Sobolev spaces $W^{s,p}$ with $p>1$ for arbitrary Gromov hyperbolic groups. These are closed subspaces of $L^p$ and in particular Hilbert spaces in…

We investigate geometric properties of a metric measure space where every function in the Newton--Sobolev space $N^{1,\infty}(Z)$ has a Lipschitz representative. We prove that when the metric space is locally complete and the reference…

We study a characterization of BV and Sobolev functions via nonlocal functionals in metric spaces equipped with a doubling measure and supporting a Poincar\'e inequality. Compared with previous works, we consider more general functionals.…

We study limits at infinity for homogeneous Hajlasz-Sobolev functions defined on uniformly perfect metric spaces equipped with a doubling measure. We prove that a quasicontinuous representative of such a function has a pointwise limit at…

The unique solvability of parabolic equations in Sobolev spaces with mixed norms is presented. The second order coefficients (except $a^{11}$) are assumed to be only measurable in time and one spatial variable, and VMO in the other spatial…

In this paper we will focus on understanding the relation between Sobolev embedding theorems for Haj{\l}asz-Besov spaces defined on a doubling metric measure space $(\Omega,d,\mu)$ and the non-collapsing condition of the measure, i.e. \[…

Reparametrization invariant Sobolev metrics on spaces of regular curves have been shown to be of importance in the field of mathematical shape analysis. For practical applications, one usually discretizes the space of smooth curves and…

In a complete metric space that is equipped with a doubling measure and supports a Poincar\'e inequality, we prove a new Cartan-type property for the fine topology in the case $p=1$. Then we use this property to prove the existence of…

We establish two new characterizations of magnetic Sobolev spaces for Lipschitz magnetic fields in terms of nonlocal functionals. The first one is related to the BBM formula, due to Bourgain, Brezis, and Mironescu. The second one is related…

This paper gives a systematic study of Sobolev, Besov and Triebel-Lizorkin spaces on a noncommutative $d$-torus $\mathbb{T}^d_\theta$ (with $\theta$ a skew symmetric real $d\times d$-matrix). These spaces share many properties with their…

We present isocapacitary characterizations of Sobolev inequalities in very general metric measure spaces.

We study completeness properties of Sobolev metrics on the space of immersed curves and on the shape space of unparametrized curves. We show that Sobolev metrics of order $n\geq 2$ are metrically complete on the space $\mathcal…

An apparently new concept of maximal mean difference quotient is defined for functions in the Lebesgue space $L_{loc}(R^n)$. Our definitions are meaningful for vector valued functions on general measure metric spaces as well and seem to…

In this paper, we characterize parabolic Besov and parabolic Sobolev spaces in ${\bf R}^{n+1}$ and ${\bf R}^{n+1}_T, \,\, T > 0$. We also, study the relation between parabolic Besov spaces in ${\bf R}^{n}_T, \,\, T > 0$ and standard Besov…

We introduce a variational first-order Sobolev calculus on metric measure spacetimes. The key object is the maximal weak subslope of an arbitrary causal function, which plays the role of the (Lorentzian) modulus of its differential. It is…

We show that the first order Sobolev spaces on cuspidal symmetric domains can be characterized via pointwise inequalities. In particular, they coincide with the Hajlasz-Sobolev spaces.

We characterize the restrictions of first order Sobolev functions to regular subsets of a homogeneous metric space and prove the existence of the corresponding linear extension operator.

In this article, we study the relation between Sobolev-type embeddings for Sobolev spaces or Besov spaces or Triebel-Lizorkin spaces defined either on a doubling or on a geodesic metric measure space and lower bound for measure of balls…

Kuelbs-Steadman spaces are introduced in this article on a separable metric space with finite diameter and finite positive Borel measure. Kuelbs-Steadman spaces of the Lipschitz type are also discussed. Various inclusion properties are also…

We define the chain Sobolev space on a possibly non-complete metric measure space in terms of chain upper gradients. In this context, $\varepsilon$-chains are a finite collection of points with distance at most $\varepsilon$ between…