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I want to solve the equation: $$ \begin{cases} \nabla \times (A \mathbf v)=f, \quad x\in \Omega \\ \operatorname{div}(\mathbf v)=0, \end{cases} $$ where $\Omega \subset\mathbb{R}^n$, is an open set, $...

I wonder if there is any references for the study of the following type of spaces $$ X_{\delta,\alpha}=\{ u\in L^2_\delta(\mathbb{R}^n):\, u= (-\Delta)^\alpha f \quad\text{for some}\quad f\in L^2_{\...