The fractional S-transform on BMO and Hardy spaces

TL;DR

This paper investigates the properties of the fractional S-transform within BMO and Hardy spaces, extending previous results and analyzing its behavior on weighted variants of these function spaces.

Contribution

It generalizes existing results on the fractional S-transform, providing new continuity and boundedness results on BMO and Hardy spaces, including their weighted versions.

Findings

Established boundedness of the fractional S-transform on BMO and Hardy spaces.

Extended the analysis to weighted BMO and Hardy spaces.

Generalized previous results to broader function space settings.

Abstract

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.