BMO spaces related to Laguerre semigroups

ELEONOR HARBOURE; ANIBAL CHICCO RUIZ

MATHEMATISCHE NACHRICHTEN

WILEY-V C H VERLAG GMBH

Lugar: Weinheim; Año: 2013

0025-584X

For the system of Laguerre functions $\{\varphi_n^\alpha\}$ we define a suitable $BMO$ space from the atomic space $H^1_{\varphi^\alpha}= \{f\in L^1:\Wphi f \in L^1\}$ considered by Dziubasnki in \cite{Dzi}, where $\Wphi$ is maximal operatorassociated to the Heat Semigroup of the Laguerre functions. We provethe boundedness of $\Wphi$ for a weighted version of that $BMO$, andwe extend this result for the system of Laguerre functions$\{\mathcal{L}^\alpha_n\}$. Also, we generalize those kind of $BMO$spaces and we prove boundedness on them for the local version ofHardy-Littlewood and Heat-Diffusion maximal operators.