Multilinear Stockwell transforms

University Politehnica of Bucharest, Department of Mathematics-Informatics, Spl. Independenţei 313, 060042 Bucharest, Romania

^* Corresponding author: catana_viorel@yahoo.co.uk

Received: 29 November 2017
Accepted: 1 February 2018

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 L^p(Rⁿ) and also on the Hörmander’s spaces B_p,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.