The dual of Besov spaces on fractals

For certain classes of fractal subsets F of ${\displaystyle {ℝ}^n}$, the Besov spaces ${\displaystyle B_{\alpha }^{p,q}\left(F\right)}$ have been studied for α > 0 and 1 ≤ p,q ≤ ∞. In this paper the Besov spaces ${\displaystyle B_{\alpha }^{p,q}\left(F\right)}$ are introduced for α < 0, and it is shown that the dual of ${\displaystyle B_{\alpha }^{p,q}\left(F\right)}$ is !$!B_{-α}^{p',q'}(F), α ≠ 0, 1 < p,q < ∞, where 1/p + 1/p' = 1, 1/q + 1/q' = 1.