Weighted norm inequalities for the Littlewood–Paley function in domains with cone-points

The classes $\mathscr H_\alpha^p(\Omega)$ of harmonic functions in a domain $\Omega$, $\Omega\subset\mathbb R^n$, $n\ge3$, with finite number of cone-points are introduced. The weighted analogue of the well-known Littlewood–Paley inequality for corresponding functions in $\Omega$ is proved.