Hankel–Clifford transformations on some ultradifferentiable function spaces and pseudo-differential operators

Abstract

Continuity of the first Hankel–Clifford transformation on the spaces of the type \(H_\mu \) are investigated. Pseudo-differential operator \(h_{1,\mu ,a}\) associated with Bessel type operator \(xD_{x}^{2}+(1-\mu )D_{x}\) involving the symbol \(a(x,y)\) whose derivatives satisfy certain growth conditions depending on some increasing sequences, is studied on certain ultradifferentiable function spaces. It is shown that the operator \(h_{1,\mu ,a}\) is a continuous linear mapping of one ultradifferentiable function spaces into another spaces of same type.