Admissible changes of variables in the class of BMO functions
Let \(\phi\) be a function (not necessarily monotone) which maps an interval P into itself. The author gives sufficient conditions for \(\phi\) to guarantee that \((*)\;\{f\in BMO(P)\Rightarrow f\circ \phi \in BMO(P)\}.\) The conditions are complicated and not easy to verify for a concrete function. Earlier, \textit{P. Jones} [Ark. Mat. 21, 229-231 (1983; Zbl 0527.42007)] gave necessary and sufficient conditions implying (*) when \(\phi\) is a homeomorphism of the real line. The author shows that for monotone convex functions \(\phi\) on the real line his condition is also necessary and is equivalent to \(\phi\) being quasisymmetric.
scientific article; zbMATH DE number 4198753
scientific article