The boundedness on $ BMO_{L_\alpha} $ space of variation operators for semigroups related to the Laguerre operator

Fan Chen; Houwei Du; Jinglan Jia; Ping Li; Zhu Wen; Fan Chen; Houwei Du; Jinglan Jia; Ping Li; Zhu Wen

doi:10.3934/math.20241093

AIMS Mathematics

2024, Volume 9, Issue 8: 22486-22499. doi: 10.3934/math.20241093

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Research article

The boundedness on $ BMO_{L_\alpha} $ space of variation operators for semigroups related to the Laguerre operator

1.
Department of mathematics and health care, Yangtze University College of Arts and Sciences, Jingzhou 434000, China
2.
School of Information and Mathematics, Yangtze University, Jingzhou 434000, China

Received: 15 April 2024 Revised: 06 July 2024 Accepted: 09 July 2024 Published: 19 July 2024
MSC : 42B15, 42B20, 58J50

In this paper, we established a $ T1 $ criterion for the boundedness of Laguerre-Calderón-Zygmund operators on BMO$ _{L_{\alpha}}(0, \infty) $ associated with Laguerre operators $ L_\alpha(\alpha > -\frac{1}{2}) $. As applications, we proved the boundedness on BMO$ _{L_{\alpha}}(0, \infty) $ of variation operators for semigroups related to the Laguerre operator $ L_\alpha $.
- $ T1 $ criterion,
- BMO$ _{L_{\alpha}} $ space,
- Laguerre operators,
- semigroups,
- variation operators
Citation: Fan Chen, Houwei Du, Jinglan Jia, Ping Li, Zhu Wen. The boundedness on $ BMO_{L_\alpha} $ space of variation operators for semigroups related to the Laguerre operator[J]. AIMS Mathematics, 2024, 9(8): 22486-22499. doi: 10.3934/math.20241093

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Abstract

In this paper, we established a $ T1 $ criterion for the boundedness of Laguerre-Calderón-Zygmund operators on BMO$ _{L_{\alpha}}(0, \infty) $ associated with Laguerre operators $ L_\alpha(\alpha > -\frac{1}{2}) $. As applications, we proved the boundedness on BMO$ _{L_{\alpha}}(0, \infty) $ of variation operators for semigroups related to the Laguerre operator $ L_\alpha $.

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