Summary: We study the two-parameter family of unitary operators \[ \mathcal F_{k,a} = \exp\left(\frac{i\pi}{2a}(2 \langle k \rangle +\mathrm{d}+a-2)\right)\exp\left(\frac{i\pi}{2a} \Delta_{k,a}\right), \] which are called \((k,a)\)-generalized Fourier transforms and defined by the \(a\)-deformed Dunkl harmonic oscillator \(\Delta_{k,a}=| x|^{2-a} \Delta_k -| x|^a\), \(a>0\), where \(\Delta_k\) is the Dunkl Laplacian. Particular cases of such operators are the Fourier and Dunkl transforms. The restriction of \(\mathcal F_{k,a}\) to radial functions is given by an \(a\)-deformed Hankel transform \(H_{\lambda, a}\). We obtain necessary and sufficient conditions for the weighted \((L^p, L^q)\) Pitt inequalities to hold for the \(a\)-deformed Hankel transform. Moreover, we prove two-sided Boas-Sagher type estimates for the general monotone functions. We also prove sharp Pitt’s inequality for \(\mathcal F_{k,a}\) transform in \(L^2(\mathbb R^{\mathrm{d}})\) with the corresponding weights. Finally, we establish the logarithmic uncertainty principle for \(\mathcal F_{k,a}\).