Boundedness for Parametrized Littlewood-Paley Operators with Rough Kernels on Weighted Weak Hardy Spaces

Abstract

The authors prove that the parametrized area integral ${\mu }_{\mathrm{\Omega },S}^{\rho }$ and $g_{\lambda }^{\mathrm{*}}$ function ${\mu }_{\lambda }^{\mathrm{*},\rho }$ are bounded from the weighted weak Hardy space $W{H}_w^{\mathrm{1}}({ℝ}^n)$ to the weighted weak Lebesgue space $W{L}_w^{\mathrm{1}}({ℝ}^n)$ as $\mathrm{\Omega }$ satisfies a class of the integral Dini condition, respectively.