for all test functions f , where y′ = y/|y| ∈ Sn−1. We denote SIΩ,h( f ) by SIΩ( f ) if h= 1. The operator SIΩ was first studied by Calderón and Zygmund in their well-known papers (see [1, 2]). They proved that SIΩ is Lp(Rn) bounded, 1 < p < ∞, provided that Ω ∈ LLog+L(Sn−1) satisfying (1.1). They also showed that the space LLog+L(Sn−1) cannot be replaced by any Orlicz space Lφ(Sn−1) with a mon...