论文标题
在$ s \至0^+$的限制上
On the limit as $s\to 0^+$ of fractional Orlicz-Sobolev spaces
论文作者
论文摘要
在Orlicz空间设置中，建立了Maz'ya-shaposhnikova定理的限制为$ s \ to 0^+$的$ s \ to 0^+$。我们的结果在与满足$Δ_2$ - 条件的年轻功能相关的分数Orlicz-Sobolev空间中，并且如反例所示，如果此条件删除，则可能会失败。
An extended version of the Maz'ya-Shaposhnikova theorem on the limit as $s\to 0^+$ of the Gagliardo-Slobodeckij fractional seminorm is established in the Orlicz space setting. Our result holds in fractional Orlicz-Sobolev spaces associated with Young functions satisfying the $Δ_2$-condition, and, as shown by counterexamples, it may fail if this condition is dropped.
