Hankel-Clifford transformations on some ultradifferentiable function spaces and pseudo-differential operators (Q2254346)

The authors study a class of pseudodifferential operators, based on using, instead of the Fourier transform, the so-called first Hankel-Clifford transformation \[ \hat{\varphi}(y)=y^\mu \int\limits_0^\infty C_\mu (xy)\varphi (x)\,dx, \] where \(\mu \geq 0\), \(C_\mu (x)=x^{-\mu /2}J_\mu (2x^{1/2})\), \(J_\mu\) is the Bessel function. For appropriate classes of symbols and function spaces, continuity conditions for such pseudodifferential operators are found.