Maximal operators for the holomorphic Laguerre semigroup

• Autores: E. Sasso
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 97, Nº 2, 2005, págs. 235-265
• Idioma: inglés
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• Resumen

  • 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.