Inner superposition operator in spaces of integrable functions. (Russian) Zbl 0605.47032
The author studies the operator
\[
(Sx)(t)=A(t)(S_ gx)(t)
\]
in the spaces \(L_ p(\Omega,{\mathbb{R}}^ n)\) and \(L_{\infty}(\Omega,{\mathbb{R}}^ n)\), where A is a matrix function and \((S_ gx)(t)=x(g(t))\) is the inner superposition operator generated by a function g on \(\Omega\).
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.) |
