Structure, boundedness, and convergence in the dual of a Hankel-K{Mp} space

Hankel-K{M-p} spaces, as introduced by the second-named author, play the same role in the theory of the Hankel transformation as the Gelfand-Shilov K{M-p} spaces in the theory of the Fourier transformation. For mu > -1/2, under suitable restrictions on the weights {M-p}(infinity)(p=0), the topology of a Hankel-K{M-p} space E can be generated by norms of L-q-type (1 <= q <= infinity) involving the Bessel operator S-mu. In this paper, adapting a technique due to Kaminski, the elements of the dual space E' are represented as S-mu-distributional derivatives of a single continuous function. Corresponding characterizations of boundedness and convergence in (the weak, weak*, strong topologies of) E' are obtained.