Littlewood-Paley characterization of discrete Morrey spaces and its application to the discrete martingale transform
Abstract
The goal of this paper is to develop the Littlewood–Paley theory of discrete Morrey spaces. As an application, we establish the boundedness of martingale transforms. We carefully justify the definition of martingale transforms, since discrete Morrey spaces do not contain discrete Lebesgue spaces as dense subspaces. We also obtain the boundedness of Riesz potentials.
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