论文标题
仿射分数Sobolev和Isoperimetric不平等现象
Affine Fractional Sobolev and Isoperimetric Inequalities
论文作者
论文摘要
建立了对$ \ Mathbb r^n $功能的急剧仿射分数的不平等现象。对于每个$ 0 <s <1 $，新的不平等现象明显比（直接暗示）Almgren和Lieb的急剧分数Sobolev不平等。在$ s \至1^ - $的限制中，新的不平等意味着高阳张的敏锐的offine sobolev不平等。因此，获得了比分数欧几里得等等的不等式的分数投影不平等，证明了径向平均体的自然猜想。
Sharp affine fractional Sobolev inequalities for functions on $\mathbb R^n$ are established. For each $0<s<1$, the new inequalities are significantly stronger than (and directly imply) the sharp fractional Sobolev inequalities of Almgren and Lieb. In the limit as $s\to 1^-$, the new inequalities imply the sharp affine Sobolev inequality of Gaoyong Zhang. As a consequence, fractional Petty projection inequalities are obtained that are stronger than the fractional Euclidean isoperimetric inequalities and a natural conjecture for radial mean bodies is proved.
