A capacity associated with the weighted Lebesgue space and its applications (Q2120177)

Summary: In this paper, we focus on a further study of the weighted Lebesgue capacity associated with the following fractional heat equation: \[ \begin{cases} \left( \partial_t + \left( -\Delta_x\right)^\alpha\right) u \left( t, x\right) = 0,\ \forall \left( \alpha, t, x\right) \in \left( 0,1\right) \times \left( 0, \infty\right) \times \mathbb{R}^n, \\ u \left( 0, x\right) = f \left( x\right),\ \forall x \in \mathbb{R}^n. \end{cases} \] More properties of that capacity are explored, and applications to a trace inequality for the weak solution of the equation are considered.