On the transformation dual to the Radon–Kipriyanov transformation

The Radon–Kipriyanov transformation $K_\gamma$ was introduced in 1998. In various theoretical and applied research, the dual transformation $K_\gamma^{\#}$ is required. We prove theorems on the boundedness of the dual transformation in the corresponding L. Schwarz subspace of test functions and the $K_\gamma^{\#}$-transformation of the convolution of a function $g$ with the $K_\gamma[f]$-transformation, provided that both functions $g$ and $f$ belong to the corresponding spaces of test functions.