Hardy type inequalities for Aharonov-Bohm magnetic potentials with multiple singularities (Q1429215)

A. Laptev and T. Weidl proved the Hardy-type inequality \[ \int_{R^2}\frac{| u(x)|^2}{| x|^2} \,dx\leq C\int_{R^2}| (\nabla +\imath A)u(x)| ^2 \,dx , \] with the sharp constant \(C\) for \(u\in C^{\infty}_0(R^2\setminus \{0\})\) and a smooth magnetic vector potential \(A\) in \(R^2\setminus \{0\}\) with \(\operatorname{curl} A=0\). The present author extends this result to magnetic Dirichlet forms with Aharonov-Bohm vector potentials in \(R^2\) having multiple singularities.