Journal of the
Korean Mathematical Society JKMS

Under the cancellation property and the Lipschitz condition on kernels, we prove that the Marcinkiewicz integrals defined on a homogeneous group $\mathbb{H}$ are bounded from $H^{1}\left(\mathbb{H}\right)$ to $L^{1}\left(\mathbb{H}\right)$, from $L_{c}^\infty\left(\mathbb{H}\right)$ to $BMO\left(\mathbb{H}\right)$, and from $L^{p}\left(\mathbb{H}\right)$ to $L^{p}\left(\mathbb{H}\right)$ for $1

Keywords: Marcinkiewicz integrals, homogeneous groups

MSC numbers: Primary 42B20; Secondary 47B38