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Nemytskii operator on $$(\phi ,2,\alpha )$$ ( ϕ , 2 , α ) -bounded variation space in the sense of Riesz
Journal of Pseudo-Differential Operators and Applications ( IF 0.9 ) Pub Date : 2020-09-15 , DOI: 10.1007/s11868-020-00366-8 René E. Castillo , Edixon M. Rojas , Eduard Trousselot
中文翻译:
Riesz意义上的$$(\ phi,2,\ alpha)$$(ϕ,2,α)有界变化空间上的Nemytskii算符
更新日期:2020-09-15
Journal of Pseudo-Differential Operators and Applications ( IF 0.9 ) Pub Date : 2020-09-15 , DOI: 10.1007/s11868-020-00366-8 René E. Castillo , Edixon M. Rojas , Eduard Trousselot
In this paper we show that if the Nemytskii operator maps the \((\phi ,2,\alpha )\)-bounded variation space into itself and satisfies some Lipschitz condition, then there are two functions g and h belonging to the \((\phi ,2,\alpha )\)-bounded variation space such that \(f(t,y)=g(t)y+h(t)\) for all \(t\in [a,b]\), \(y\in {\mathbb {R}}\).
中文翻译:
Riesz意义上的$$(\ phi,2,\ alpha)$$(ϕ,2,α)有界变化空间上的Nemytskii算符
在本文中,我们证明了如果Nemytskii运算符将\((\ phi,2,\ alpha)\)有界的变化空间映射到其自身中并且满足一些Lipschitz条件,则存在两个函数g和h属于\( (\ phi,2,\ alpha)\)有界的变化空间,使得[a,b]中所有\(t \ )的\(f(t,y)= g(t)y + h(t)\)\),\(y \ in {\ mathbb {R}} \)中。