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

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 $.

Keywords

• $ t1 $ criterion
• bmo$ _{l_{\alpha}} $ space
• laguerre operators
• semigroups
• variation operators