On $L^p$ bounds for the Littlewood-Paley $g_{\alpha }$ function with fractional poisson kernel

Hui Li, Ziyuan Lian, Honghai Liu +2

Let \(0<α\leq1\), and let \(g_α\) be the Littlewood-Paley function associated with the fractional Poisson kernel, which reduces to the classical \(g\)-function when \(α=1\). We est…