SUBSTITUTION OPERATORS IN THE SPACES OF FUNCTIONS OF BOUNDED VARIATION BV2α(I)
SUBSTITUTION OPERATORS IN THE SPACES OF FUNCTIONS OF BOUNDED VARIATION BV2α(I)
The space <TEX>$BV^2_{\alpha}(I)$</TEX> of all the real functions defined on interval <TEX>$I=[a,b]{\subset}\mathbb{R}$</TEX>, which are of bounded second <TEX>${\alpha}$</TEX>-variation (in the sense De la Vall<TEX>$\acute{e}$</TEX> Poussin) on I forms a Banach space. In this space we define an operator of substitution H generated by a function <TEX>$h:I{\times}\mathbb{R}{\rightarrow}\mathbb{R}$</TEX>, and prove, in particular, …