Mlak, W. Operators induced by transformations of Gaussian variables. (English) Zbl 0606.47035 Ann. Pol. Math. 46, 197-212 (1985). The author studies the inner superposition operator \(T_ af(x)=f(a(x))\), generated by some absolutely continuous strictly increasing real function a, in \(L^ 2\) spaces with weight \(e^{-x^ 2/2}\). By standard tensor products, the results (in particular, estimates and formulas for the norm of \(T_ a)\) carry over to higher dimensions. Reviewer: J.Appell Cited in 6 Documents MSC: 47B38 Linear operators on function spaces (general) 46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) Keywords:inner superposition operator; absolutely continuous strictly increasing real function; tensor products PDFBibTeX XMLCite \textit{W. Mlak}, Ann. Pol. Math. 46, 197--212 (1985; Zbl 0606.47035) Full Text: DOI