McKennon-type spaces for the Hankel transformation (Q2565234)

For \(\mu>-{1\over 2}\), the Zemanian space \({\mathcal H}_\mu\) of Hankel transformable functions is expressed as the projective limit of a chain \(\{{\mathcal S}^p_\mu\}_{p\in\mathbb{N}}\) of reflexive Banach spaces, where the Hankel transformation is an isometric isomorphism. In this paper, motivated by [\textit{K. McKennon}, Czech. Math. J. 29(104), 503-513 (1979; Zbl 0432.46039)] the study developed in [the authors, Appl. Anal. 52, No. 1-4, 103-124 (1994; Zbl 0840.46020)] is carried out with \(L^1\)-norms instead of \(L^2\)-norms.