Abstract In this paper, we study the Lp 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 conseque...Abstract In this paper, we study the Lp 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 Lp boundedness of various maximal oscillatory singular integrals provided that their kernels belong to the natural space L log L（Sn-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.展开更多
文摘Abstract In this paper, we study the Lp 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 Lp boundedness of various maximal oscillatory singular integrals provided that their kernels belong to the natural space L log L（Sn-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.
