Parametrized Littlewood–Paley operators on Hardy and weak Hardy spaces

In this paper, we give the boundedness of the parametrized Littlewood–Paley function $ \mu ^{*,\rho}_{\lambda} $ on the Hardy spaces and weak Hardy spaces. As the corollaries of the above results, we prove that $ \mu ^{*,\rho}_{\lambda} $ is of weak type (1, 1) and of type ( p , p ) for 1 < p < 2, respectively. This results are substantial improvement and extension of some known results. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)