Resumen de Maximal operators for the holomorphic Laguerre semigroup

E. Sasso

• For each p in [1,∞) let Ep denote the closure of the region of holomorphy of the Laguerre semigroup {Mαt:t>0} on Lp with respect to the Laguerre measure μα. We prove weak type and strong type estimates for the maximal operator f↦sup{|Mαzf|:z∈Ep}. In particular, we give a new proof for the weak type 1 estimate for the maximal operator associated to Mαt. Our starting point is the well-known relationship between the Laguerre semigroup of half-integer parameter and the Ornstein-Uhlenbeck semigroup.