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A Primer on Carnot Groups: Homogenous Groups, Carnot-Carathéodory Spaces, and Regularity of Their Isometries

100%

Le Donne E.

Analysis and Geometry in Metric Spaces

2017

tom 5

nr 1

116-137

Carnot groups are distinguished spaces that are rich of structure: they are those Lie groups equipped with a path distance that is invariant by left-translations of the group and admit automorphisms that are dilations with respect to the distance. We present the basic theory of Carnot groups together with several remarks.We consider them as special cases of graded groups and as homogeneous metric spaces.We discuss the regularity of isometries in the general case of Carnot-Carathéodory spaces and of nilpotent metric Lie groups.

Some remarks on Bochner-Riesz means

100%

Thangavelu S.

Colloquium Mathematicum

2000

tom 83

nr 2

217-230

We study $L^p$ norm convergence of Bochner-Riesz means $S_R^δ f$ associated with certain non-negative differential operators. When the kernel $S_R^m(x,y)$ satisfies a weak estimate for large values of m we prove $L^p$ norm convergence of $S_R^δ f$ for δ > n|1/p-1/2|, 1 < p < ∞, where n is the dimension of the underlying manifold.

Ograniczanie wyników

1 Analysis and Geometry in Metric Spaces

1 Colloquium Mathematicum

1 Le Donne E.

1 Thangavelu S.

1 2017

1 2000

Wyniki wyszukiwania

A Primer on Carnot Groups: Homogenous Groups, Carnot-Carathéodory Spaces, and Regularity of Their Isometries

Some remarks on Bochner-Riesz means