论文标题
关于霍尔德空间嵌入到高斯空间中的清晰度
On the sharpness of embeddings of Hölder spaces into Gaussian Besov spaces
论文作者
论文摘要
对于带有$ e_1 \ e_1 \ hookrightArrow e_0 $的Banach空间的插值对$（e_0，e_1）$，我们使用矢量$ b_1，b_2，b_2，\ ldots \在e_1 $中，可以满足$ j $ - j $ - 和$ k $ - 功能为$ j $ uncluctional to subsuctional to subsuctional to subsuctional to subsuctions subsuctions subsuck的$ subspace usopt $; eell_elt $}的极端属性。该结构基于使用独立的Rademacher变量的随机化。我们验证通过重新缩放具有一定周期性属性的函数获得的系统共享此极端属性。这意味着通过将实际插值插入相应的高斯BESOV空间中获得的Hölder空间的天然嵌入的清晰度。
For an interpolation pair $(E_0,E_1)$ of Banach spaces with $E_1 \hookrightarrow E_0$ we use vectors $b_1,b_2,\ldots \in E_1$ that satisfy an extremal property with respect to the $J$- and $K$-functional to construct sub-spaces that are isometric to $\ell_q^{(θ)}$. The construction is based on a randomisation using independent Rademacher variables. We verify that systems obtained by re-scaling a function with a certain periodicity property share this extreme property. This implies the sharpness of natural embeddings of Hölder spaces obtained by the real interpolation into the corresponding Gaussian Besov spaces.
