| Abstract: | In this paper,we study the L~p mapping properties of certain class of maximal oscillatory singular integral operators.We prove a general theorem for a class of maximal functions along surfaces.As a consequence of such theorem,we establish the L~p boundedness of various maximal oscillatory singular integrals provided that their kernels belong to the natural space L log L(S~(n-1)).Moreover,we highlight some additional results concerning operators with kernels in certain block spaces.The results in this paper substantially improve previously known results. |
