| Summary: | Abstract In this paper we consider a singular integral operator and a parametric Marcinkiewicz integral operator with rough kernel. These operators have singularity along sets of the form curves {x=P(φ(|y|))y′} $\{x=P(\varphi (|y|))y'\}$, where P is a real polynomial satisfying P(0)=0 $P(0)=0$ and φ satisfies certain smooth conditions. Under the conditions that Ω∈H1(Sn−1) $\varOmega \in H^{1} (\mathbf{S}^{n-1})$ and h∈Δγ(R+) $h\in \Delta _{\gamma }(\mathbf{R}_{+})$ for some γ>1 $\gamma >1$, we prove that the above operators are bounded on the Lebesgue space L2(Rn) $L^{2}( \mathbf{R}^{n})$. Moreover, the L2 $L^{2}$-bounds of the maximal functions related to the above integrals are also established. Particularly, the bounds are independent of the coefficients of the polynomial P. In addition, we also present certain Hardy type inequalities related to these operators.
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