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Operators induced by transformations of Gaussian variables. (English) Zbl 0606.47035

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

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.)
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