A note on the generalized Marcinkiewicz integral operators with rough kernels (Q1941302)

The authors study the generalized Marcinkiewicz integral operators \(M_{\Omega,r}\) on the product space \({\mathbb R}^n\times{\mathbb R}^m\). Under the condition that \(\Omega\) is a function in certain block spaces, which is optimal in some senses, the boundedness of such operators from Triebel-Lizorkin spaces to \(L^p\) spaces is obtained. Their result is not contained in the past result concerned with the condition of \(\Omega\).