A New Approach to $(1,1)-$Weak-type Estimate for the Littlewood-Paley Operators $S_{\alpha ,\psi }$ and $g_{\lambda ,\psi }^{\ast }$

In this study, $(1,1)-$weak type boundedness of square function $S_{\alpha ,\psi }$ is obtained by using Nazarov-Treil and Volberg technique. Also using this result, the $(1,1)-$ weak type boundedness of $g_{\lambda ,\psi }^{\ast }$ operator is investigated.