  In this paper, the authors studied the fractional S-transform on BMO and
Hardy spaces and generalized the results given in \cite{Singh15h}. In
introduction section, the definitions of the S-transform, fractional Fourier
transform and fractional S-transform are given. In Section 2 continuity and
boundedness results for the fractional S-transform in BMO and Hardy spaces are
obtained. Furthermore, in Section 3 the fractional S-transform is studied on
the weighted BMO$_{\kappa}$ and weighted Hardy spaces associated with a
tempered weight function.
