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

摘要

Continuity of the first Hankel-Clifford transformation on the spaces of the type H_μ are investigated. Pseudo-differential operator h_(1,μ,α) associated with Bessel type operator xD_x~2 + (1 -μ)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 operatorh_(1,μ,α) is a continuous linear mapping of one ultradifferentiable function spaces into another spaces of same type.