Math. Model. Nat. Phenom.
Volume 13, Number 4, 2018
|Number of page(s)||11|
|Published online||21 May 2018|
Multilinear Stockwell transforms
University Politehnica of Bucharest, Department of Mathematics-Informatics,
Spl. Independenţei 313,
* Corresponding author: firstname.lastname@example.org
Accepted: 1 February 2018
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.
Mathematics Subject Classification: 42C40 / 47G10
Key words: Fourier transforms / Stockwell transforms / pseudo-differential operators / uncertainty principle
© EDP Sciences, 2018
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