Singular integral operators and maximal functions with Hardy space kernels

In this paper, we study singular integrals along compound curves with Hardy space kernels. We introduce a class of bidirectional generalized Hardy Littlewood maximal functions. We prove that the considered singular integrals and the maximal functions are bounded on L^p, 1 < p<∞ provided that the compound curves are determined by generalized polynomials and convex increasing functions. The obtained results offer L^p estimates that are not only new but also they generalize as well as improve previously known results.