Admissible changes of variables in the class of BMO functions
type: Item
instance of: scholarly article
title: Admissible changes of variables in the class of BMO functions
zbMATH Open document ID: 0726.42014
DOI: 10.1007/BF01158842
author: M. A. Fominykh
published in: Mathematical Notes
publication date: 1988-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 42B30
Mathematics Subject Classification ID: 46E99
zbMATH DE Number: 4198753
zbMATH Keywords: changes of variables
zbMATH Keywords: BMO functions
zbMATH Keywords: monotone convex functions
zbMATH Keywords: quasisymmetric
MaRDI profile type: Publication
cites work: On functions of bounded mean oscillation
cites work: Q3874458
cites work: Q3922907
cites work: On the transformation of functions of bounded mean oscillation
cites work: Homeomorphisms of the line which preserve BMO
cites work: Bounded mean oscillation with Orlicz norms and duality of Hardy spaces
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description: scientific article; zbMATH DE number 4198753