Bourgain–Brezis–Mironescu convergence via Triebel-Lizorkin spaces
Bourgain–Brezis–Mironescu convergence via Triebel-Lizorkin spaces
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DOI：
10.1007/s00526-022-02382-6
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发表时间：
2021-09
影响因子：
2.1
通讯作者：
Denis Brazke;A. Schikorra;Po-Lam Yung
中科院分区：
文献类型：
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作者：
Denis Brazke;A. Schikorra;Po-Lam Yung
利用Triebel-Lizorkin空间研究了Bourain-Brezis-Mironescu(BBM)的一个收敛结果。众所周知，空格和。当经脉变成经脉时，但BBM表明经脉变成了经脉。天真地说，这似乎是一个矛盾，但我们通过提供关于的尖锐常量来嵌入FOF来解决这个问题。作为结果，我们得到了BBM-结果的一个-版本，并得到了几个据我们所知未知的BBM型嵌入和收敛定理。
We study a convergence result of Bourgain–Brezis–Mironescu (BBM) using Triebel-Lizorkin spaces. It is well known that as spaces, and. When, thenorm becomes thenorm but BBM showed that thenorm becomes thenorm. Naively, forthis seems like a contradiction, but we resolve this by providing embeddings ofintoforwith sharp constants with respect to. As a consequence we obtain an-version of the BBM-result, and obtain several more embedding and convergence theorems of BBM-type that to the best of our knowledge are unknown.