论文标题
组成运算符进入有限变化的功能空间
Composition operator into the space of function of bounded variation
论文作者
论文摘要
令$ω_1，ω_2\ subset \ mathbb r^n $和$ 1 \ leq p <\ infty $。我们研究同构$ f：ω_1$ to $ω_2$上的最佳条件，该条件保证了$ u \ circ f $属于w^{1，p}中的每个$ u \ in $ u \ u \ u \ in p}（p}（ω_2）$的空间$ bv（ω_1）$。我们表明，足够和必要的条件是在l^{p'}（ω_2）$中的函数$ k（y）\的存在，因此所有borel sets $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $的$ | df |（f^{ - 1}（a））\ leq \ int_a k（y）\，dy $。
Let $Ω_1, Ω_2\subset \mathbb R^n$ and $1\leq p <\infty$. We study the optimal conditions on a homeomorphism $f:Ω_1$ onto $Ω_2$ which guarantee that the composition $u\circ f$ belongs to the space $BV(Ω_1)$ for every $u\in W^{1,p}(Ω_2)$. We show that the sufficient and necessary condition is an existence of a function $K(y)\in L^{p'}(Ω_2)$ such that $|Df|(f^{-1}(A))\leq \int_A K(y)\,dy$ for all Borel sets $A$.
