Boehmian space for certain generalized integral transformation

Abstract

The classical $\mathfrak{F}_{a}^{b}$ transform was proclaimed as an
extension to Fourier and Hartley transformations. In $\left[ 17\right] ,$
authors have extended the $\mathfrak{F}_{a}^{b}$ transform to a space of
generalized functions and they further have obtained some desired properties. This article discusses the $\mathfrak{F}_{a}^{b}$ transform on certain space of generalized functions. Two spaces of Boehmians have been established and the extended $\mathfrak{F}_{a}^{b}$ transform is also defined. Some general properties of the transform are given in some detail.