We study the two-parameter family of unitary operators Fk,a=exp(iπ2a(2〈k〉+d+a−2))exp(iπ2aΔk,a), which are called -generalized Fourier transforms and defined by the -deformed Dunkl harmonic oscillator , , where is the Dunkl Laplacian. Particular cases of such operators are the Fourier and Dunkl transforms. The restriction of to radial functions is given by an -deformed Hankel transform . We obtain necessary and sufficient conditions for the weighted Pitt inequalities to hold for the -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 transform in with the corresponding weights. Finally, we establish the logarithmic uncertainty principle for .