| Popis: |
For the system of Laguerre functions we define a suitable BMO space from the atomic version of the Hardy space considered by Dziubanski in [7], where is the maximal operator of the heat semigroup associated to that Laguerre system. We prove boundedness of over a weighted version of that BMO, and we extend such result to other systems of Laguerre functions, namely and . To do that, we work with a more general family of weighted BMO-like spaces that includes those associated to all of the above mentioned Laguerre systems. In this setting, we prove that the local versions of the Hardy-Littlewood and the heat-diffusion maximal operators turn to be bounded over such family of spaces for weights. This result plays a decisive role in proving the boundedness of Laguerre semigroup maximal operators. |
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