I. Marrero [Integral Transforms Spec. Funct. 13, 379–401 (2002; Zbl 1027.46040)] introduced Hankel-\(K\{M_p\}\) spaces, which are Fréchet spaces playing the same role with respect to the Hankel transform as the Gelfand-Shilov spaces with respect to the Fourier transform. The main result of the paper shows that continuous linear functionals on Hankel-\(K\{M_p\}\) spaces can be represented as \(S_\mu\)-derivatives of a single continuous function, where \(\mu > -\frac{1}{2}\) and \(S_\mu = x^{-\mu-\frac{1}{2}}Dx^{2\mu + 1}Dx^{-x-\frac{1}{2}}.\) Characterizations of boundedness and convergence in the dual of Hankel-\(K\{M_p\}\) spaces in terms of the Bessel differential operator are also obtained.