On a Class of Singular Integral Operators With Rough Kernels

http://dx.doi.org/10.4153/CMB-2006-001-9
Canad. Math. Bull. 49(2006), 3-10

  Published:2006-03-01
 Printed: Mar 2006

In this paper, we study the $L^p$ mapping properties of a class of singular integral operators with rough kernels belonging to certain block spaces. We prove that our operators are bounded on $L^p$ provided that their kernels satisfy a size condition much weaker than that for the classical Calder\'{o}n--Zygmund singular integral operators. Moreover, we present an example showing that our size condition is optimal. As a consequence of our results, we substantially improve a previously known result on certain maximal functions.