  We revise Cwikel-type estimate for the singular values of the operator
$(1-\Delta_{\mathbb{T}^d})^{-\frac{d}{4}}M_f(1-\Delta_{\mathbb{T}^d})^{-\frac{d}{4}}$
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 $d.$
