Zobrazeno 1 - 10
of 132
pro vyhledávání: '"VÄHÄKANGAS, ANTTI V."'
We prove that a pointwise fractional Hardy inequality implies a fractional Hardy inequality, defined via a Gagliardo-type seminorm. The proof consists of two main parts. The first one is to characterize the pointwise fractional Hardy inequality in te
Externí odkaz:
http://arxiv.org/abs/2404.05222
We study non-local or fractional capacities in metric measure spaces. Our main goal is to clarify the relations between relative Hajlasz-Triebel-Lizorkin capacities, potentional Triebel-Lizorkin capacities, and metric space variants of Riesz capaciti
Externí odkaz:
http://arxiv.org/abs/2403.12513
Autor:
Kline, Josh, Vähäkangas, Antti V.
We present a new notion, the upper Aikawa codimension, and establish its equivalence with the upper Assouad codimension in a metric space with a doubling measure. To achieve this result, we first prove variant of a local fractional Hardy inequality.
Externí odkaz:
http://arxiv.org/abs/2311.12748
We prove weighted inequalities between the Gagliardo and Sobolev seminorms and also between the Marcinkiewicz quasi-norm and the Sobolev seminorm. With $A_1$ weights we improve earlier results of Bourgain, Brezis, and Mironescu.
Externí odkaz:
http://arxiv.org/abs/2302.14029
We examine the class of weakly porous sets in Euclidean spaces. As our first main result we show that the distance weight $w(x)=\operatorname{dist}(x,E)^{-\alpha}$ belongs to the Muckenhoupt class $A_1$, for some $\alpha>0$, if and only if $E\subset\
Externí odkaz:
http://arxiv.org/abs/2209.06284
We examine the relations between different capacities in the setting of a metric measure space. First, we prove a comparability result for the Riesz $(\beta,p)$-capacity and the relative Hajlasz $(\beta,p)$-capacity, for $1
Externí odkaz:
http://arxiv.org/abs/2208.14732
In this paper we unify and improve some of the results of Bourgain, Brezis and Mironescu and the weighted Poincar\'e-Sobolev estimate by Fabes, Kenig and Serapioni. More precisely, we get weighted counterparts of the Poincar\'e-Sobolev type inequalit
Externí odkaz:
http://arxiv.org/abs/2201.11712
Publikováno v:
In Journal of Functional Analysis 15 October 2024 287(8)
Autor:
Canto, Javier, Vähäkangas, Antti V.
We prove a self-improvement property of a capacity density condition for a nonlocal Hajlasz gradient in complete geodesic spaces. The proof relates the capacity density condition with boundary Poincar\'e inequalities, adapts Keith-Zhong techniques fo
Externí odkaz:
http://arxiv.org/abs/2108.09077
We prove fractional Sobolev-Poincar\'e inequalities, capacitary versions of fractional Poincar\'e inequalities, and pointwise and localized fractional Hardy inequalities in a metric space equipped with a doubling measure. Our results generalize and e
Externí odkaz:
http://arxiv.org/abs/2108.07209