We consider one-sided weight classes of Muckenhoupt type and study the weighted weak type (1,1) norm inequalities of a class of one-sided oscillatory singular integrals with smooth kernel.
We consider singular integral operators and maximal singular integral operators with rough kernels on homogeneous groups. We prove certain estimates for the operators that imply $L^p$ boundedness of them by an extrapolation argument under a sharp con
dition for the kernels. Also, we prove some weighted $L^p$ inequalities for the operators.
We prove certain $L^p$ estimates ($1<p<infty$) for non-isotropic singular integrals along surfaces of revolution. As an application we obtain $L^p$ boundedness of the singular integrals under a sharp size condition on their kernels.
