BMO-boundedness of maximal operators and \(g\)-functions associated with Laguerre expansions
For the Laguerre differential operator \(L_\alpha\), the authors study the boundedness on BMO\(_{L_\alpha}\) of \(M_+\), the classical Hardy-Littlewood maximal operator on \(\mathbb R^+\). They consider similar estimates for the heat maximal function \(T^*_\alpha f(x)=\sup_{t>0}|T_t^\alpha f(x)|\), and the Littlewood-Paley \(g\)-function, associated to the heat-diffusion semigroup \(\{T_t^\alpha\}_{t\geq0}\) generated by \(-L_{\alpha}\) (under the restriction \(\alpha>-1/2\)). Related results can be found, for Schrödinger operators on \(\mathbb R^d\) (\(d\geq3\)), in [\textit{J. Dziubański} et al., Math. Z. 249, No. 2, 329--356 (2005; Zbl 1136.35018)], and also, on a different type of BMO space, in [\textit{D. C. Yang}, \textit{D. Y. Yang}, and \textit{Y. Zhou}, Commun. Pure Appl. Anal. 9, No. 3, 779--812 (2005; Zbl 1188.42008)].
scientific article; zbMATH DE number 6102743
scientific article