Authors: AHMAD AL SALMAN

Abstract: 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 <\infty $ 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.

Keywords: Singular integrals, Hardy space, compound curves, Hardy Littlewood maximal function, convex functions

Full Text: PDF