Lp-improving measures on compact non-abelian groups

Journal of the Australian Mathematical Society

Kathryn E. Hare¹ 

关键词: 43 A 05;    43 A 46;   

DOI  :  10.1017/S1446788700030895

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

A Borel measure μ on a compact group G is called Lp-improving if the operator Tμ: L2(G) → L2(G), defined by Tμ(f) = μ * f, maps into Lp(G) for some P > 2. We characterize Lp-improving measures on compact non-abelian groups by the eigenspaces of the operator Tμ if |Tμ|. This result is a generalization of our recent characterization of Lp-improving measures on compact abelian groups.Two examples of Riesz product-like measures are constructed. In contrast with the abelian case one of these is not Lp-improving, while the other is a non-trivial example of an Lp improving measure.

【 授权许可】

Unknown