Marcinkiewicz integral on Hardy spaces (Q5957558)

The authors prove that the Marcinkiewicz integrals with kernel satisfying \(L^1\)-Dini condition are bounded from the Hardy space \(H^1(\mathbb R^n)\) into \(L^1(\mathbb R^n)\), and that if the kernel satisfies a stronger Dini-type condition, then the corresponding Marcinkiewicz integrals are also bounded from \(H^{1,\infty}(\mathbb R^n)\) into \(L^{1,\infty}(\mathbb R^n)\).