We consider a singular second order differential operator defined on . We give nice estimates for the kernel which intervenes in the integral transform of the eigenfunction of . Using these results, we establish Hardy type inequalities for Riemann-Liouville and Weyl transforms associated with the operator .
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defined on ![$ ]0,infty[$](images/211_04_JIPAM/img2.gif){kind=small}
. We give nice estimates for the kernel which intervenes in the integral transform of the eigenfunction of 
