Maximal operators for the holomorphic Laguerre semigroup - Sasso, Emanuela (MATHEMATICA SCANDINAVICA, 2005)
For each p in [1,∞) let E_p denote the closure of the region of holomorphy of the Laguerre semigroup {M^α_t:t>0} on L^p with respect to the Laguerre measure μ_α. We prove weak type and strong type estimates for the maximal operator f{|M^α_z f|:zE_p}. In particular, we give a new proof for the weak type 1 estimate for the maximal operator associated to M^α_t. Our starting point is the well-known relationship between the Laguerre semigroup of half-integer parameter and the Ornstein-Uhlenbeck semigroup.