$BMO$ Spaces for Laguerre Expansions
$BMO$ Spaces for Laguerre Expansions
Let $\{\varphi_n^{\alpha}\}_{n \in \mathbb{N}}$ be the Laguerre functions of Hermite type with index $\alpha$. These are eigenfunctions of the Laguerre differential operator $L_\alpha = \dfrac{1}{2}(-\frac{d^2}{dy^2} + y^2 + \frac{1}{y^2}(\alpha^2-\frac{1}{4}))$. We define and study a $BMO$-type space $BMO_{L_{\alpha}}$, which is identified as the dual space of the Hardy-type space associated with …