We prove certain L estimates (1 < p <∞) for non-isotropic singular integrals along surfaces of revolution. The singular integrals are defined by rough kernels. As an application we obtain L boundedness of the singular integrals under a sharp size condition on their kernels. We also prove a certain estimate for a trigonometric integral, which is useful in studying non-isotropic singular integrals.

We establish the L boundedness of singular integrals on product domains with rough kernels in L(logL) and are supported by subvarieties.

In this paper, we establish an Lp boundedness result of a class of Marcinkiewicz integral operators on product domains with rough kernels.

We obtain a quantitative weighted bound for the Calderón commutator $\mathcal C_\Omega $ which is typical example of non-convolution Calderón–Zygmund operator under condition $\Omega \in L^\infty (\mathbb S^{n-1})$; this best known quantita