Under study are the homeomorphisms that induce the bounded composition operators of \( BV \)-functions on Carnot groups. We characterize continuous \( BV_{\operatorname{loc}} \)-mappings on Carnot groups in terms of the variation on integral lines and estimate the variation of the \( BV \)-derivative of the composition of a \( C^{1} \)-function and a continuous \( BV_{\operatorname{loc}} \)-mapping.

中文翻译：

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$ BV $ -空间和$ BV $的有界复合算子 -卡诺群上的函数

正在研究的是卡诺群上的\(BV\) -函数的有界复合算子的同态。我们 根据积分线上的变化来表征卡诺群上的 连续\( BV_{\operatorname{loc}} \)映射，并估计 \ ( C^的组成的 \( BV \) -导数的变化{1} \) -函数和连续 \( BV_{\operatorname{loc}} \) -映射。