Harmonic analysis problems associated with the \(k\)-Hankel Gabor transform (Q2210470)

The authors introduce a continuous \(k\)-Hankel Gabor transform acting on a Hilbert space deforming \(L^2(\mathbb{R})\). They prove two fundamental properties of the \(k\)-Hankel Gabor transform, viz., the Plancherel formula and the \(L^2\)-inversion formula. These properties are crucial in proving a large class of weighted inequalities for this transform. The authors also obtain various uncertainty principles such as the Heisenberg uncertainty principle, Nash uncertainty principle, Faris-Price uncertainty principle, and Donoho-Stark uncertainty principle for this transform.