Generalized Pitt’s inequality for the Gabor transform

The generalized forms of Pitt’s inequality for the $$$L^p$$$-Gabor transform on the groups of the form $$$ℝ^n; ℝ^n \times K, K$$$ being a Lie group of type I, in particular, a connected nilpotent Lie group; Heisenberg motion group and diamond Lie groups have been established.

The generalized forms of Pitt’s inequality for the $$$L^p$$$-Gabor transform on the groups of the form $$$ℝ^n; ℝ^n \times K, K$$$ being a Lie group of type I, in particular, a connected nilpotent Lie group ; Heisenberg motion group and diamond Lie groups have been established.

Diamond Lie groups Fourier transform Gabor transform Hausdorff-Young inequality Heisenberg motion group Nilpotent Lie groups Pitt’s inequality

Diamond Lie groups Fourier transform Gabor transform Hausdorff-Young inequality Heisenberg motion group Nilpotent Lie groups Pitt’s inequality