On NEMYTSKIJ Operators in Lp‐Spaces of Abstract Functions
Copyright policy )On NEMYTSKIJ Operators in Lp‐Spaces of Abstract Functions
AbstractThis paper is concerned with continuity and differentiability of NEMYTSKIJ operators acting between spaces of summable abstract functions. In a first part, necessary and sufficient conditions for continuity are collected. Then main emphasis is given to sufficient conditions for differentiability in the sense of FRÉCHET and GÂTEAUX. Finally, second order differentiability is briefly discussed.
- Chemnitz University of Technology Germany
- University of Greifswald Germany
Nemytskij operators between Bochner-Lebesgue spaces, Particular nonlinear operators (superposition, Hammerstein, Nemytskiĭ, Uryson, etc.), continuity, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.), differentiability
Nemytskij operators between Bochner-Lebesgue spaces, Particular nonlinear operators (superposition, Hammerstein, Nemytskiĭ, Uryson, etc.), continuity, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.), differentiability
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