PARAMETRIC MARCINKIEWICZ INTEGRAL OPERATORS AND COMMUTATORS ON HERZ-HARDY SPACES WITH VARIABLE EXPONENTS

In this paper, the authors obtain the boundedness of parametric Marcinkiewicz integral operator with variable kernel and its commutators on Herz spaces with variable exponents $ \dot{\mathcal{K}}_{p(\cdot)}^{\alpha(\cdot), q(\cdot)}(\mathbb{R}^{n}) $ when the parameters $ \alpha(\cdot), p(\cdot) $ and $ q(\cdot) $ satisfies some conditions. Meanwhile, the corresponding estimates on Herz-Hardy spaces with variable exponents $ H\dot{\mathcal{K}}_{p(\cdot)}^{\alpha(\cdot), q(\cdot)}(\mathbb{R}^{n}) $ are also established.