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Generalized local Morrey spaces and multilinear commutators generated by Marcinkiewicz integrals with rough kernel associated with Schr\"{o}dinger operators and local Campanato functions
Keywords:Marcinkiewicz operator, rough kernel, Schr\"{o}dinger operator, generalized local Morrey space, multilinear commutator.
Abstract:
      Let $L=-\Delta+V\left( x\right) $ be a Schr\"{o}dinger operator, where $\Delta$ is the Laplacian on ${\mathbb{R}^{n}}$, while nonnegative potential $V\left( x\right) $ belongs to the reverse H\"{o}lder class. In this paper, we consider the behavior of multilinear commutators of Marcinkiewicz integrals with rough kernel associated with Schr\"{o}dinger operators on generalized local Morrey spaces.