Taiwanese Journal of Mathematics

$BMO$ Spaces for Laguerre Expansions

Li Cha and Heping Liu

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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 $L_{\alpha}$. We characterize $BMO_{L_{\alpha}}$ by Carlesson measures related to appropriate square functions. Finally, we prove the boundedness on this space of the fractional integral operator and the Riesz transform related to $L_{\alpha}$.

Article information

Taiwanese J. Math., Volume 16, Number 6 (2012), 2153-2186.

First available in Project Euclid: 18 July 2017

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Zentralblatt MATH identifier

Primary: 42C05: Orthogonal functions and polynomials, general theory [See also 33C45, 33C50, 33D45] 42B35: Function spaces arising in harmonic analysis 30H35: BMO-spaces

$BMO$ space Laguerre expansions Carlesson measures fractional integral operator Riesz transform


Cha, Li; Liu, Heping. $BMO$ Spaces for Laguerre Expansions. Taiwanese J. Math. 16 (2012), no. 6, 2153--2186. doi:10.11650/twjm/1500406845. https://projecteuclid.org/euclid.twjm/1500406845

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