Estimates for parameter Littlewood-Paley \(g_\kappa^\ast\) functions on nonhomogeneous metric measure spaces (Q288779)

This paper studies the mapping properties of the parameter \(g^{\ast}_{\kappa}\) functions on nonhomogeneous metric measure spaces. The Marcinkiewicz integrals and the parameter Littlewood-Paley functions are members of the family of the parameter \(g^{\ast}_{\kappa}\) functions. This paper obtains the boundedness of the parameter \(g^{\ast}_{\kappa}\) functions on Lebesgue spaces and on the atomic Hardy spaces.