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 condition for the kernels. Also, we prove some weighted $L^p$ inequalities for the operators.
A bilinear sparse domination for the maximal singular integral operators with rough kernels
The $L(\log L)^ε$ endpoint estimate for maximal singular integral operators
An endpoint estimate for the commutators of singular integral operators with rough kernels
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