Weighted estimates for Marcinkiewicz integrals with applications to angular integrability

Abstract

We establish the weighted estimates for the parametric Marcinkiewicz integral operators with rough kernels along “polynomial curves” on $$\\mathbb {R}^n$$\n . As applications, we obtain that the above operators are bounded on the mixed radial-angular spaces, on the vector-valued mixed radial-angular spaces and on the vector-valued function spaces. Particularly, the above bounds are independent of the coefficients of the polynomials in the definition of the operators.