论文标题
有限变化功能的组成操作员
Composition operator for functions of bounded variation
论文作者
论文摘要
我们研究同构$ f：ω\ subset \ r^n \ to \ r^n $的最佳条件，以确保构图$ u \ circ f $属于每个函数变化的函数函数$ u $ u $ u $ u $ u $ u $的函数。我们表明，足够且必要的条件是存在常数$ k $，因此所有borel set $ a $ a $ $ | df |（f^{ - 1}（a））\ leq k \ ln（a）$。我们还表征同构的同态，这些形态映射到有限周围的有限周长。在这些结果方面，我们研究$ f^{ - 1} $映射集的零态度集零（即$ f $满足lusin $（n^{ - 1}）$条件）。
We study the optimal conditions on a homeomorphism $f:Ω\subset \R^n\to \R^n$ to guarantee that the composition $u\circ f$ belongs to the space of functions of bounded variation for every function $u$ of bounded variation. We show that a sufficient and necessary condition is the existence of a constant $K$ such that $|Df|(f^{-1}(A))\leq K\Ln(A)$ for all Borel sets $A$. We also characterize homeomorphisms which maps sets of finite perimeter to sets of finite perimeter. Towards these results we study when $f^{-1}$ maps sets of measure zero onto sets of measure zero (i.e. $f$ satisfies the Lusin $(N^{-1})$ condition).
