We consider the generalized Littlewood-Paley square functions arising from rough kernels and prove the -boundedness for a certain range of depending on the kernel. We also study a class of singular integrals by similar methods.
"Remarks on Littlewood-Paley functions and singular integrals." J. Math. Soc. Japan 54 (3) 565 - 585, July, 2002. https://doi.org/10.2969/jmsj/1191593909