论文标题
增强了Besov空间中的分数Sobolev型不平等
Strengthened Fractional Sobolev Type Inequalities in Besov Spaces
论文作者
论文摘要
本文的目的是双重的。首先是通过经典的Lorentz空间加强BESOV空间中的分数Sobolev型不平等。在这样做的过程中，我们表明，BESOV空间中的Sobolev不平等等同于分数硬性不平等和异常类型的不平等。其次，我们将通过与BESOV能力相关的电容性Lorentz空间来加强BESOV空间中的分数Sobolev型不平等。为此，我们首先研究了相关的洛伦兹相关的洛伦兹空间与古典洛伦兹空间的嵌入。然后，建立了将BESOV空间嵌入到电容性Lorentz空间中的嵌入。同时，我们表明，这些嵌入与新引入的分数$（β，p，q）$ - 周长有关，与ISO-opacity型不平等密切相关。此外，还建立了BESOV空间中更一般的Sobolev类型不平等的特征。
The purpose of this article is twofold. The first is to strengthen fractional Sobolev type inequalities in Besov spaces via the classical Lorentz space. In doing so, we show that the Sobolev inequality in Besov spaces is equivalent to the fractional Hardy inequality and the iso-capacitary type inequality. Secondly, we will strengthen fractional Sobolev type inequalities in Besov spaces via capacitary Lorentz spaces associated with Besov capacities. For this purpose, we first study the embedding of the associated capacitary Lorentz space to the classical Lorentz space. Then, the embedding of the Besov space to the capacitary Lorentz space is established. Meanwhile, we show that these embeddings are closely related to the iso-capacitary type inequalities in terms of a new-introduced fractional $(β, p, q)$-perimeter. Moreover, characterizations of more general Sobolev type inequalities in Besov spaces have also been established.
