Boundedness of Marcinkiewicz Integral and Its Commutators on Variable Exponent Weak $$\lambda$$-Central Morrey Spaces

In this paper, we first introduce the variable exponent weak $$\lambda$$ -central Morrey spaces $$W\dot{\mathcal{M}}^{q(\cdot),\lambda}(\mathbb{R}^{n})$$ and study its basic properties. Moreover, the boundedness of parametric Marcinkiewicz integral operator with variable kernel and its commutators from variable exponent $$\lambda$$ -central Morrey spaces $$\dot{\mathcal{M}}^{q(\cdot),\lambda}(\mathbb{R}^{n})$$ to variable exponent weak $$\lambda$$ -central Morrey spaces $$W\dot{\mathcal{M}}^{q(\cdot),\lambda}(\mathbb{R}^{n})$$ are obtained.