论文标题
最佳Sobolev嵌入的不同程度的非紧密度
Different degrees of non-compactness for optimal Sobolev embeddings
论文作者
论文摘要
定量研究了$ m $ thording的最佳Sobolev嵌入订单中的非紧缩性的结构，并在所有重排空间中的lebesgue空间中的结构进行了定量研究。获得了此类嵌入的伯恩斯坦数量的尖锐的双向估计。结果表明，尽管Lebesgue空间中的最佳SOBOLEV嵌入有限的奇异性，但最佳的Sobolev嵌入了所有重排式式函数空间的类别中，甚至都不是严格的单数。
The structure of non-compactness of optimal Sobolev embeddings of $m$-th order into the class of Lebesgue spaces and into that of all rearrangement-invariant function spaces is quantitatively studied. Sharp two-sided estimates of Bernstein numbers of such embeddings are obtained. It is shown that, whereas the optimal Sobolev embedding within the class of Lebesgue spaces is finitely strictly singular, the optimal Sobolev embedding in the class of all rearrangement-invariant function spaces is not even strictly singular.
