We prove sharp upper and lower bounds for generalized Calderón's sums associated to frames on LCA groups generated by affine actions of cocompact subgroup translations and general measurable families of automorphisms. The proof makes use of techniques of analysis on metric spaces, and relies on a counting estimate of lattice points inside metric balls. We will deduce as special cases Calderón-type inequalities for families of expanding automorphisms as well as for LCA-Gabor systems.

中文翻译：

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仿射帧的Calderón型不等式

我们证明了与LCA群上的框架相关的广义Calderón和的尖锐上下界，这些LCA群是由协紧凑子群翻译的仿射动作和一般可测同构同族产生的。该证明利用了对度量空间的分析技术，并依赖于对度量球内部晶格点的计数估计。作为特殊情况，我们将推导扩展自同构族以及LCA-Gabor系统的Calderón型不等式。