A weak inequality in fractional homogeneous Sobolev spaces

Lifeng Wang

For $s\in \mathbb{R}$ and $0<q<\infty$, we denote \begin{equation*} \mathcal{D}_{s,q}f(x):=\big(\int_{\mathbb{R}^n}\frac{|f(x)-f(y)|^q}{|x-y|^{n+sq}}dy\big)^{\frac{1}{q}}. \end{equa…