Abstract
In this paper, we introduce the
k
-generalized Stockwell transform on
R
. We investigate for this transform the main theorems of Harmonic analysis as Plancherel’s, Calderón’s, and inversion formulas. Next, we prove several uncertainty principles for this transform such as Heisenberg’s type inequalities, Shannon’s uncertainty principle, Benedick–Amrein–Berthier’s uncertainty principle, and local uncertainty principles. Finally, after reviewing the
k
-generalized weighted inequalities, we connect these inequalities to show a generalization of uncertainty principles for the
k
-generalized Stockwell transform.