Littlewood-Paley \(g\)-functions and multipliers for the Laguerre hypergroup
The differential operator \[ L=-\bigg(\frac{\partial^2}{\partial x^2}+ \frac{2\alpha+1}{x} \frac{\partial}{\partial x} + x^2 \frac{\partial^2}{\partial t^2} \bigg) \] and the generated Laguerre hypergroup \(K\) are considered. It is proved that the corresponding Littlewood-Paley \(g\)-function is bounded on \(L_p(K)\), \(1<p<\infty\). The Hörmander multiplier theorem is also proved.
scientific article; zbMATH DE number 5887697