Bounded Linearness of Distributional Generalized Hankel-Schwartz Type Transformations on \(L^{'}_{p,v}\) Spaces

Abstract

Two Hankel-Schwartz type transformations are defined in this study. On the L_p,v and \(L^{'}_{p,v}\) spaces, the Hankel-Schwartz type transformations are defined. It is also demonstrated that the transformations defined by (1) and (2) are bounded linear operators of L_p,v. We also study the behaviour of transformations defined by (3) and (4) on the L_p,v spaces. It is also shown that the transformations defined by (3) and (4) are bounded linear operator of L_p,v into L_{p,2p(3\(\alpha\)+\(\beta\))-v} and of L _p,v into L_{p,-v-2(\(\alpha\)-\(\beta\))p} respectively. Finally, we proved that distributional generalised HankelSchwartz type transformation on \(L^{'}_{p,v}\) spaces are bounded linear.