Lebesgue-Riesz norm estimates for fractional Laplace transform
  We obtain in this short article the bilateral non-asymptotic estimations for the norm in Lebesgue-Riesz and bilateral Grand Lebesgue spaces of the so-called fractional Laplace integral transform.   We give also examples to show the sharpness of these inequalities. 
E.Ostrovsky, L.Sirota
math.FA