Inequalities for generalized parametric Marcinkiewicz integrals along polynomial compound curves

摘要

Under some weaker size conditions assumed on the integral kernels both on the unitsphere and in the radial directions, the sharp Lp boundedness was proved for the generalizedparametric Marcinkiewicz integrals along polynomial compound curves via an extrapolation argument.As applications, the corresponding results for generalized parametric Marcinkiewiczintegral operators related to the Littlewood-Paley g?λ -functions and area integrals are also established.