Under weak conditions on the kernels, we obtain sharp Lp bounds for rough parabolic maximal integral operators over surfaces of revolution. By virtue these along with Yano’s extrapolation argument, confirm boundedness under weaker kernels. Our obtained results represent substantial extensions and improvements some known kernels symmetric spaces.

In this paper, local and global kernels are combined to use the detailed and rough similarities simultaneously. In recent years, many recognition methods based on local features have been proposed. However, the combination of only local matching is not sufficient. Global viewpoint is also necessary to improve the generalization ability. In general, local feature matching measures the detailed s...

In this note, we study singular integrals with rough kernels, which belong to a class of singular Radon transforms. We prove certain estimates for the singular integrals that are useful in an extrapolation argument. As an application, we prove L p boundedness of the singular integrals under a certain sharp size condition on their kernels.