Multilinear Stockwell transforms

Abstract

The main aim of this paper is to introduce multilinear versions of the Stockwell transforms (also named S-transforms) by using the fact that S-transforms can be written as convolution products. Further on we extend the multilinear S-transforms from the Schwartz class of rapidly decreasing functions to the space of tempered distributions. In the sequel we give a relation between multilinear S-transforms and multilinear pseudo-differential operators. We also state and prove some boundedness results regarding multilinear S-transforms on the Lebegue’s spaces Lp(Rn) and also on the Hörmander’s spaces Bp,k(Rn), where p ≥ 1 and k is a temperate weight function. In the end, a weak uncertainty principle for multilinear S-transforms and for its adjoint is also given.