Intrinsic metrics and Lipschitz functions
Copyright policy )Intrinsic metrics and Lipschitz functions
The author studies the notion of measurable metrics and Lipschitz functions w.r.t. such metrics -- originally introduced by \textit{N. Weaver} [Stud. Math. 115, 277-289 (1995; Zbl 0839.46014)] -- on Dirichlet structures and, in particular, abstract Wiener spaces. In the latter case it is shown that the intrinsic metric [in the sense of \textit{M. Biroli} and \textit{U. Mosco}, Ann. Math. Pura Appl. 169, 125-181 (1995; Zbl 0851.31008)] coincides with Weaver's measurable metric. For more general local Dirichlet structures supporting a carré du champ operator this is still an open problem. In the setting of such Dirichlet spaces the Lipschitz-continuous functions in \(L^2\) and \(L^\infty\) are characterized in terms of the carré du champ operator which, in the case of abstract Wiener spaces, leads to a new characterization of Enchev-and-Stroock's H-Lipschitz functions [\textit{O. Enchev} and \textit{D. W. Stroock}, Ann. Probab. 21, 25-33 (1993; Zbl 0773.60042)].
Dirichlet forms, Spaces of differentiable or holomorphic functions on infinite-dimensional spaces, Lipschitz function, abstract Wiener space, intrinsic metric, Stochastic analysis, carré du champ operator, Sub-Riemannian geometry, Banach spaces of continuous, differentiable or analytic functions, Dirichlet form, measurable metric
Dirichlet forms, Spaces of differentiable or holomorphic functions on infinite-dimensional spaces, Lipschitz function, abstract Wiener space, intrinsic metric, Stochastic analysis, carré du champ operator, Sub-Riemannian geometry, Banach spaces of continuous, differentiable or analytic functions, Dirichlet form, measurable metric
citations This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).11 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!