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

Abstract

ABSTRACT Hankel- spaces, as introduced by the second-named author, play the same role in the theory of the Hankel transformation as the Gelfand-Shilov spaces in the theory of the Fourier transformation. For , under suitable restrictions on the weights , the topology of a Hankel- space E can be generated by norms of -type involving the Bessel operator . In this paper, adapting a technique due to Kamiński, the elements of the dual space are represented as -distributional derivatives of a single continuous function. Corresponding characterizations of boundedness and convergence in (the weak, weak*, strong topologies of) are obtained.