Lp Bounds for Rough Maximal Operators along Surfaces of Revolution on Product Domains

In this paper, we study the boundedness of rough Maximal integral operators along surfaces of revolution on product domains. For several classes of surfaces, we establish appropriate L-P bounds of these Maximal operators under the assumption Omega is an element of L-q (Sm-1 x S-1) for some >1, and then we employ these bounds along with Yano's extrapolation argument to obtain the L-P boundedness of the aforementioned integral operators under a weaker condition in which Omega belongs to either the space B-q((0),(2/tau'-1))(S(m-1)xS(n-1))) or to the space L(log L)(2/tau)'(Sm- x Sn-1). Our results extend and improve many previously known results.