论文标题
Cwikel-Solomyak对托里和欧几里得空间的估计
Cwikel-Solomyak estimates on tori and Euclidean spaces
论文作者
论文摘要
我们修订了操作员$（1-δ_ {\ Mathbb {t}^d}）^{ - \ frac {d} {4}} m_f（1-δ__{\ m at { $ \ mathbb {t}^d $用于理想$ \ mathcal {l} _ {1，\ infty} $，由M.Z建立。在\ cite {Solomyak1995}中的均匀尺寸中的Silomyak，并将其扩展到奇数。我们为$ \ mathbb {r}^d $ in tunyrary正整数$ d。$ d。$ d。
We revise Cwikel-type estimate for the singular values of the operator $(1-Δ_{\mathbb{T}^d})^{-\frac{d}{4}}M_f(1-Δ_{\mathbb{T}^d})^{-\frac{d}{4}}$ on the torus $\mathbb{T}^d$ for the ideal $\mathcal{L}_{1,\infty}$, established by M.Z. Solomyak in even dimensions in \cite{Solomyak1995}, and extend it to odd dimensions. We obtain a new result for (symmetrized) Cwikel type estimates for Laplacians on $\mathbb{R}^d$ for arbitrary positive integer $d.$
