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2012 $BMO$ Spaces for Laguerre Expansions
Li Cha, Heping Liu
Taiwanese J. Math. 16(6): 2153-2186 (2012). DOI: 10.11650/twjm/1500406845

Abstract

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 $L_{\alpha}$.

Citation

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Li Cha. Heping Liu. "$BMO$ Spaces for Laguerre Expansions." Taiwanese J. Math. 16 (6) 2153 - 2186, 2012. https://doi.org/10.11650/twjm/1500406845

Information

Published: 2012
First available in Project Euclid: 18 July 2017

zbMATH: 1264.42004
MathSciNet: MR3001841
Digital Object Identifier: 10.11650/twjm/1500406845

Subjects:
Primary: 30H35, 42B35, 42C05

Rights: Copyright © 2012 The Mathematical Society of the Republic of China

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Vol.16 • No. 6 • 2012
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