On Rough Parametric Marcinkiewicz Integrals Along Certain Surfaces

This work focuses on investigating rough Marcinkiewicz integrals associated to specific surfaces. Whenever the kernel functions belong to Lq(Sm−1) space, the Lp boundedness of these Marcinkiewicz integrals is confirmed. This finding along with Yano’s extrapolation argument prove the Lp boundedness of the aforementioned integrals under weaker conditions on the kernels. The results in this work improve and generalize various previously known results on Marcinkiewicz integrals.