We consider maximal singular integral operators arising from rough kernels satisfying an H^1-type condition on the unit (n-1)-sphere and prove weighted L^p estimates for certain radial weights. We also prove weighted L^p estimates with A_p-weights where in this case the H^1 -type condition is replaced by an L^q-type condition with q > 1. Some applications of these results are also obtained regarding singular integrals and Marcinkiewicz integrals. Our results are essential extensions and improvements of some known results.
L^p boundedness, Hardy space, maximal operators, Fourier transform, rough kernel, A_p weight
AL-QASSEM, HUSSAIN (2006) "Weighted Norm Inequalities for a Class of Rough Maximal Operators," Turkish Journal of Mathematics: Vol. 30: No. 4, Article 6. Available at: https://journals.tubitak.gov.tr/math/vol30/iss4/6