Abstract
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.
