An extended version of the Maz’ya–Shaposhnikova theorem on the limit as \(s\rightarrow 0^+\) 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 \(\Delta _2\)-condition, and, as shown by counterexamples, it may fail if this condition is dropped.

中文翻译：

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在$$ s \ rightarrow 0 ^ + $$ s→0 +的分数阶Orlicz–Sobolev空间上

在Orlicz空间设置中，建立了Gazardo-Slobodeckij分数半范数\（s \ rightarrow 0 ^ + \）极限的Maz'ya–Shaposhnikova定理的扩展版本。我们的结果保存在与满足\（\ Delta _2 \）-条件的Young函数关联的分数Orlicz-Sobolev空间中，并且如反示例所示，如果删除此条件，则它可能会失败。