In this paper, we establish the boundedness of parameterized Littlewood-Paley operator μλ^＊,p and parameterized area integralμΩ^σSp with kernel satisfying the logarithmic type Lipschitz condition on the weak Hardy space.
In this paper, we obtain the（W Hω^1, W Lω^1） type estimate for the Marcinkiewicz integral and the（W H1 b,ω, W L1ω） type estimate for the commutator generated by a BMO function and the Marcinkiewicz integral, where the kernel satisfies a certain logarithmic type Lipschitz condition.
