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In this paper, we focus on a further study of the weighted Lebesgue capacity associated with the following fractional heat equation:  ∂ t + − Δ x α u t , x = 0 ,   ∀ α , t , x ∈ 0,1 × 0 , ∞ × ℝ n , u 0 , x = f x ,   ∀ x ∈ ℝ n . . More properties of that capacity are explored, and applications to a trace inequality for the weak solution of the equation are considered.

A Capacity Associated with the Weighted Lebesgue Space and Its Applications