The multivariate De Pril transform

In the present paper we extend the definition of the De Pril transform to a class of multivariate functions and discuss various properties of this multivariate De Pril transform. In particular, we show that, like in the univariate case, it is additive for convolutions, and discuss De Pril transforms of compound functions and higher order functions. Finally, we introduce a multivariate Dhaene–De Pril transform, which we compare with the De Pril transform.