This paper is concerned with certain multilinear commutators of BMO functions and multilinear singular integral operators with non-smooth kernels. By the sharp maximal functions estimates, the weighted norm inequalities for this kind of commutators are established.
In this paper, the author studies a class of non-standard commutators with higher order remainders for oscillatory singular integral operators with phases more general than polynomials. For 1 < p < ∞, the Lp-boundedness of such operators are obtained provided that their kernels belong to the spaces Lq(Sn-1) for some q > 1.
In this paper, the authors study the mapping properties of singular integrals on product domains with kernels in L(log+L)ε(Sm-1 × Sn-1) (ε = 1 or 2) supported by hyper-surfaces. The Lp bounds for such singular integral operators as well as the related Marcinkiewicz integral operators are established, provided that the lower dimensional maximal function is bounded on Lq(R3) for all q > 1. The condition on the integral kernels is known to be optimal.
